<?xml version="1.0"?>
<ownershipDocument>

    <schemaVersion>X0206</schemaVersion>

    <documentType>3</documentType>

    <periodOfReport>2021-07-23</periodOfReport>

    <noSecuritiesOwned>0</noSecuritiesOwned>

    <issuer>
        <issuerCik>0001856525</issuerCik>
        <issuerName>Core &amp; Main, Inc.</issuerName>
        <issuerTradingSymbol>CNM</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001759120</rptOwnerCik>
            <rptOwnerName>CD&amp;R Investment Associates X, Ltd.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O CLAYTON, DUBILIER &amp; RICE, LLC</rptOwnerStreet1>
            <rptOwnerStreet2>375 PARK AVENUE, 18TH FLOOR</rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10152</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001871836</rptOwnerCik>
            <rptOwnerName>CD&amp;R Fund X Waterworks B1, L.P.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O CLAYTON, DUBILIER &amp; RICE, LLC</rptOwnerStreet1>
            <rptOwnerStreet2>375 PARK AVENUE, 18TH FLOOR</rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10152</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001871835</rptOwnerCik>
            <rptOwnerName>CD&amp;R Fund X-A Waterworks B, L.P.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O CLAYTON, DUBILIER &amp; RICE, LLC</rptOwnerStreet1>
            <rptOwnerStreet2>375 PARK AVENUE, 18TH FLOOR</rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10152</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001871833</rptOwnerCik>
            <rptOwnerName>CD&amp;R Waterworks Holdings, L.P.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O CLAYTON, DUBILIER &amp; RICE, LLC</rptOwnerStreet1>
            <rptOwnerStreet2>375 PARK AVENUE, 18TH FLOOR</rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10152</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001728626</rptOwnerCik>
            <rptOwnerName>Core &amp; Main Management Feeder, LLC</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>1830 CRAIG PARK COURT</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>ST. LOUIS</rptOwnerCity>
            <rptOwnerState>MO</rptOwnerState>
            <rptOwnerZipCode>63146</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001871834</rptOwnerCik>
            <rptOwnerName>CD&amp;R Waterworks Holdings GP, Ltd.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O CLAYTON, DUBILIER &amp; RICE, LLC</rptOwnerStreet1>
            <rptOwnerStreet2>375 PARK AVENUE, 18TH FLOOR</rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10152</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001871837</rptOwnerCik>
            <rptOwnerName>CD&amp;R Fund X Advisor Waterworks B, L.P.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O CLAYTON, DUBILIER &amp; RICE, LLC</rptOwnerStreet1>
            <rptOwnerStreet2>375 PARK AVENUE, 18TH FLOOR</rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10152</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001874292</rptOwnerCik>
            <rptOwnerName>CD&amp;R Waterworks Holdings, LLC</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O CLAYTON, DUBILIER &amp; RICE, LLC</rptOwnerStreet1>
            <rptOwnerStreet2>375 PARK AVENUE, 18TH FLOOR</rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10152</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Class A Common Stock</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>730478</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                    <footnoteId id="F1"/>
                    <footnoteId id="F2"/>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By Affiliate</value>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Class A Common Stock</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>110828476</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                    <footnoteId id="F2"/>
                    <footnoteId id="F3"/>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By Affiliate</value>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Class A Common Stock</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>8341928</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                    <footnoteId id="F2"/>
                    <footnoteId id="F4"/>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By Affiliate</value>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Class A Common Stock</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>41847</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                    <footnoteId id="F5"/>
                    <footnoteId id="F6"/>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By Affiliate</value>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Class A Common Stock</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>8153</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                    <footnoteId id="F7"/>
                    <footnoteId id="F8"/>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By Affiliate</value>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
    </nonDerivativeTable>

    <derivativeTable>
        <derivativeHolding>
            <securityTitle>
                <value>Class B Common Stock and Limited Partnership Interests</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <footnoteId id="F9"/>
            </conversionOrExercisePrice>
            <exerciseDate>
                <footnoteId id="F9"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F9"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Class A Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>71854015</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                    <footnoteId id="F5"/>
                    <footnoteId id="F6"/>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By Affiliate</value>
                </natureOfOwnership>
            </ownershipNature>
        </derivativeHolding>
        <derivativeHolding>
            <securityTitle>
                <value>Class B Common Stock and Limited Partnership Interests</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <footnoteId id="F9"/>
            </conversionOrExercisePrice>
            <exerciseDate>
                <footnoteId id="F9"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F9"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Class A Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>13999368</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                    <footnoteId id="F7"/>
                    <footnoteId id="F8"/>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By Affiliate</value>
                </natureOfOwnership>
            </ownershipNature>
        </derivativeHolding>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">Represents securities held by CD&amp;R Fund X Advisor Waterworks B, L.P. (&quot;Fund X Advisor B&quot;).</footnote>
        <footnote id="F2">CD&amp;R Waterworks Holdings GP, Ltd. (&quot;CD&amp;R Waterworks Holdings GP&quot;), as the general partner of each of Fund X Advisor B, Fund X B1 and Fund X-A B (collectively, the &quot;CD&amp;R Blocker Fund AIVs&quot;), CD&amp;R Associates X Waterworks, L.P. (&quot;CD&amp;R Associates X&quot;), as the sole shareholder of CD&amp;R Waterworks Holdings GP, and CD&amp;R Investment Associates X, Ltd. (&quot;CD&amp;R Investment Associates&quot;), as the general partner of CD&amp;R Associates X, may be deemed to beneficially own the securities held by the CD&amp;R Blocker Fund AIVs. Each of CD&amp;R Waterworks Holdings GP, CD&amp;R Associates X and CD&amp;R Investment Associates expressly disclaims beneficial ownership of the securities held by the CD&amp;R Blocker Fund AIVs, except to the extent of its pecuniary interest therein.</footnote>
        <footnote id="F3">Represents securities held by CD&amp;R Fund X Waterworks B1, L.P. (&quot;Fund X B1&quot;).</footnote>
        <footnote id="F4">Represents securities held by CD&amp;R Fund X-A Waterworks B, L.P. (&quot;Fund X-A B&quot;).</footnote>
        <footnote id="F5">Represents securities held by CD&amp;R Waterworks Holdings, LLC (&quot;Waterworks Holdings&quot;).</footnote>
        <footnote id="F6">CD&amp;R Waterworks Holdings, L.P. (&quot;Waterworks Holdings, L.P.&quot;), as the sole member and manager of Waterworks Holdings, CD&amp;R Waterworks Holdings GP, as the general partner of Waterworks Holdings, L.P., CD&amp;R Associates X, as the sole shareholder of CD&amp;R Waterworks Holdings GP, and CD&amp;R Investment Associates, as the general partner of CD&amp;R Associates X, may be deemed to beneficially own the securities held by Waterworks Holdings. Each of Waterworks Holdings, L.P., CD&amp;R Waterworks Holdings GP, CD&amp;R Associates X and CD&amp;R Investment Associates expressly disclaims beneficial ownership of the securities held by Waterworks Holdings, except to the extent of its pecuniary interest therein.</footnote>
        <footnote id="F7">Represents securities held by Core &amp; Main Management Feeder, LLC (&quot;Management Feeder&quot;) on behalf of holders of common units of Management Feeder (the &quot;Common Units&quot;). Pursuant to the terms of, and subject to the restrictions and conditions set forth in, the Third Amended and Restated Limited Liability Company Agreement of Management Feeder, vested Common Units are redeemable at the discretion of the holder for limited partnership interests of Core &amp; Main Holdings, LP and shares of Class B common stock of the Issuer on a one-for-one basis, and have no expiration date. Upon a redemption of Common Units, a holder will also receive a distribution of the Class A common stock allocated to those Common Units.</footnote>
        <footnote id="F8">CD&amp;R Waterworks Holdings GP, as the manager of Management Feeder, CD&amp;R Associates X, as the sole shareholder of CD&amp;R Waterworks Holdings GP, and CD&amp;R Investment Associates, as the general partner of CD&amp;R Associates X, may be deemed to beneficially own the securities held by Management Feeder. Each of CD&amp;R Waterworks Holdings GP, CD&amp;R Associates X and CD&amp;R Investment Associates expressly disclaims beneficial ownership of the securities held by Management Feeder, except to the extent of its pecuniary interest therein.</footnote>
        <footnote id="F9">Pursuant to the terms of an exchange agreement, dated as of July 22, 2021, limited partnership interests of Core &amp; Main Holdings, LP, together with a corresponding number of shares of Class B common stock of the Issuer, held by the reporting persons are exchangeable at the discretion of the reporting person for shares of the Issuer's Class A common stock on a one-for-one basis, or, at the election of a majority of the disinterested members of the Issuer's board of directors, for cash from a substantially concurrent public offering or private sale (based on the price of the Issuer's Class A common stock sold in such public offering or private sale), net of any underwriting discounts and commissions, for each partnership interest exchanged, subject to certain exceptions, conditions and adjustments, and have no expiration date.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>CD&amp;R Investment Associates X, Ltd.; by: /s/ Rima Simson, Vice President, Treasurer &amp; Secretary</signatureName>
        <signatureDate>2021-07-23</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>CD&amp;R Fund X Waterworks B1, L.P.; by: CD&amp;R Waterworks Holdings GP, Ltd., the GP; by: /s/ Rima Simson, Vice President, Treasurer &amp; Secretary</signatureName>
        <signatureDate>2021-07-23</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>CD&amp;R Fund X-A Waterworks B, L.P.; by: CD&amp;R Waterworks Holdings GP, Ltd., the GP; by: /s/ Rima Simson, Vice President, Treasurer &amp; Secretary</signatureName>
        <signatureDate>2021-07-23</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>CD&amp;R Waterworks Holdings, L.P.; by: CD&amp;R Waterworks Holdings GP, Ltd., the GP; by: /s/ Rima Simson, Vice President, Treasurer &amp; Secretary</signatureName>
        <signatureDate>2021-07-23</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>Core &amp; Main Management Feeder, LLC; by: /s/ Mark Witkowski, Vice President</signatureName>
        <signatureDate>2021-07-23</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>CD&amp;R Waterworks Holdings GP, Ltd.; by: /s/ Rima Simson, Vice President, Treasurer &amp; Secretary</signatureName>
        <signatureDate>2021-07-23</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>CD&amp;R Fund X Advisor Waterworks B, L.P.; by: CD&amp;R Waterworks Holdings GP, Ltd., the GP; by: /s/ Rima Simson, Vice President, Treasurer &amp; Secretary</signatureName>
        <signatureDate>2021-07-23</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>CD&amp;R Waterworks Holdings, LLC; by CD&amp;R Waterworks Holdings, L.P., the Manager; by CD&amp;R Waterworks Holdings GP, Ltd., the GP; by: /s/ Rima Simson, Vice President, Treasurer &amp; Secretary</signatureName>
        <signatureDate>2021-07-23</signatureDate>
    </ownerSignature>
</ownershipDocument>
