Unfortunately, in your case, it sounds like you will need to file your 2020 tax return to get your payment through the Recovery Rebate Credit. The IRS used 2019 tax return data to transmit payments and there is no option to update the data for this round of payments.
You will claim the Recovery Rebate Credit in TurboTax by answering the two questions about the stimulus payments that will appear at the end of the TurboTax interview.
The questions are in the section Federal Review.
Once the information is entered you will see your refund increase or balance due decrease, and TurboTax will enter the amount of the credit on Line 30 of Form 1040 for you.