<?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>0001716691</rptOwnerCik>
            <rptOwnerName>Erfan Ali</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>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>346160</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By Ajami Associates Limited</value>
                    <footnoteId id="F1"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
    </nonDerivativeTable>

    <derivativeTable>
        <derivativeHolding>
            <securityTitle>
                <value>Warrants</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>5</value>
            </conversionOrExercisePrice>
            <exerciseDate>
                <footnoteId id="F2"/>
            </exerciseDate>
            <expirationDate>
                <value>2027-09-30</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>62500</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By Ajami Associates Limited</value>
                    <footnoteId id="F1"/>
                </natureOfOwnership>
            </ownershipNature>
        </derivativeHolding>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">The reporting person is a director of Ajami Associates Limited and may be deemed to beneficially own securities held by Ajami Associates Limited.</footnote>
        <footnote id="F2">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>
