I graduated in Dec of 2023. How do I claim a credit for using less than $10,000 from a 529 (education savings plan) plan to pay off a student loan in early 2024?

The loan question will come up later, in the 1099-Q interview. . Press Done at the 1099-Q summary screen, to get there.  Or better yet, just don't enter the 1099-Q.

You can just not report the 1099-Q, at all, if your student-beneficiary has sufficient educational expenses, including paying on a student loan, to cover the distribution. When the box 1 amount on form 1099-Q is fully covered by expenses, TurboTax will enter nothing about the 1099-Q on the actual tax forms. But, it will prepare a 1099-Q worksheet for your records (it won't help you in case of an IRS inquiry).  

References:

1. On form 1099-Q, instructions to the recipient reads: "Nontaxable distributions from CESAs and QTPs are not required to be reported on your income tax return. You must determine the taxability of any distribution." 
2. IRS Pub 970 states: “Generally, distributions are tax free if they aren't more than the beneficiary's AQEE for the year. Don't report tax-free distributions (including qualifying rollovers) on your tax return”.