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

    <schemaVersion>X0607</schemaVersion>

    <documentType>3</documentType>

    <periodOfReport>2026-06-03</periodOfReport>

    <noSecuritiesOwned>0</noSecuritiesOwned>

    <issuer>
        <issuerCik>0002091017</issuerCik>
        <issuerName>Sunshine Silver Mining &amp; Refining Co</issuerName>
        <issuerTradingSymbol>SSMR</issuerTradingSymbol>
        <issuerForeignTradingSymbol></issuerForeignTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0002132663</rptOwnerCik>
            <rptOwnerName>White Heather Eileen</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerNonUSAddressFlag>false</rptOwnerNonUSAddressFlag>
            <rptOwnerStreet1>2209 BIG CREEK RD</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>KELLOGG</rptOwnerCity>
            <rptOwnerState>ID</rptOwnerState>
            <rptOwnerZipCode>83837</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>true</isDirector>
            <isOfficer>true</isOfficer>
            <officerTitle>Chief Executive Officer</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>50000</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By White Mining Consulting Inc.</value>
                    <footnoteId id="F1"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
    </nonDerivativeTable>

    <derivativeTable>
        <derivativeHolding>
            <securityTitle>
                <value>Stock Option (Right to Buy)</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>4</value>
            </conversionOrExercisePrice>
            <exerciseDate>
                <footnoteId id="F2"/>
            </exerciseDate>
            <expirationDate>
                <value>2035-07-15</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>1463000</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeHolding>
        <derivativeHolding>
            <securityTitle>
                <value>Warrants</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>5</value>
            </conversionOrExercisePrice>
            <exerciseDate>
                <footnoteId id="F3"/>
            </exerciseDate>
            <expirationDate>
                <value>2027-09-30</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>25000</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By White Mining Consulting Inc.</value>
                    <footnoteId id="F1"/>
                </natureOfOwnership>
            </ownershipNature>
        </derivativeHolding>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">The reporting person is the President of White Mining Consulting Inc. and may be deemed to beneficially own securities held by White Mining Consulting Inc.</footnote>
        <footnote id="F2">These stock options were granted on July 15, 2025 and vest in three equal annual installments on the first three anniversaries of the grant date, subject to the reporting person's continuous service.</footnote>
        <footnote id="F3">Each warrant is exercisable for one share of common stock until the later of two years from the date of purchase or six months after the completion of the Issuer's initial public offering.</footnote>
    </footnotes>

    <remarks>Exhibit 24 - Power of Attorney.</remarks>

    <ownerSignature>
        <signatureName>/s/ Michelle Shepston, as attorney-in-fact</signatureName>
        <signatureDate>2026-06-03</signatureDate>
    </ownerSignature>
</ownershipDocument>
