Technically, if your 2023 tuition was not paid for until 2024, you do not qualify for a tuition credit.
Depending on what "my TA paid for the classes" means, it sounds like a "book keeping error" and you may want to claim the tuition credit anyway. After telling TT (TurboTax) that you do not have a 1098-T, answer yes when asked if you qualify for an exception. That will allow you to enter your expenses.
