Yes, you are correct that an amended return should be filed to claim the credit.
TurboTax will walk you through how to include the missing stimulus payment in your return. The Recovery Rebate Credit will appear on Form 1040-X, Line 7 Column B, as a change from the originally filed amount in Line 7, Column A.
For more information, see:
How do I amend my 2020 TurboTax Online return?
2020 Recovery Rebate Credit — Topic G: Correcting issues after the 2020 tax return is filed
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