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

    <schemaVersion>X0206</schemaVersion>

    <documentType>3/A</documentType>

    <periodOfReport>2023-07-20</periodOfReport>

    <dateOfOriginalSubmission>2023-07-28</dateOfOriginalSubmission>

    <noSecuritiesOwned>0</noSecuritiesOwned>

    <issuer>
        <issuerCik>0001781730</issuerCik>
        <issuerName>Third Coast Bancshares, Inc.</issuerName>
        <issuerTradingSymbol>TCBX</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001987704</rptOwnerCik>
            <rptOwnerName>Phelps David R</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>20202 HIGHWAY 59 NORTH, SUITE 190</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>HUMBLE</rptOwnerCity>
            <rptOwnerState>TX</rptOwnerState>
            <rptOwnerZipCode>77338</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <derivativeTable>
        <derivativeHolding>
            <securityTitle>
                <value>Series A Convertible Non-Cumulative Preferred Stock</value>
                <footnoteId id="F1"/>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>22.50</value>
                <footnoteId id="F3"/>
            </conversionOrExercisePrice>
            <exerciseDate>
                <value>2022-09-30</value>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F2"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                    <footnoteId id="F3"/>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>4445</value>
                    <footnoteId id="F3"/>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeHolding>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">These shares were omitted from the reporting person's original Form 3.</footnote>
        <footnote id="F2">The Series A Convertible Non-Cumulative Preferred Stock is redeemable by the Issuer (i) at any time following September 30, 2027, subject to regulatory approval and provided the closing price of the common stock has achieved certain thresholds, and (ii) at any time if the Series A Convertible Non-Cumulative Preferred Stock ceases to constitute Additional Tier 1 capital.</footnote>
        <footnote id="F3">The Series A Convertible Non-Cumulative Preferred Stock is convertible into (i) common stock, subject to certain regulatory and contractual caps, and thereafter, subject to such caps, (ii) Series B Convertible Perpetual Preferred Stock, and (iii) non-voting common stock. The Series A Convertible Non-Cumulative Preferred Stock is convertible into common stock and non-voting common stock at a price per share of $22.50, subject to certain anti-dilution adjustments, and is convertible into Series B Convertible Perpetual Preferred Stock at a rate of one share for one share.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ R. John McWhorter, attorney-in-fact</signatureName>
        <signatureDate>2023-07-31</signatureDate>
    </ownerSignature>
</ownershipDocument>
