Can I get a loan without having my W-2s?

NO.

TurboTax may have the option for a federal tax refund advance on the 2023 tax return starting in January 2024.

If they do, you do not apply for the loan.  If you are eligible it will offered to you when you have completed the 2023 federal tax return and ready to e-file the return.You can't self select it.  Then you don't get it until AFTER your efile is Accepted by the IRS.

https://turbotax.intuit.com/refund-advance/

It says......after IRS acceptance.

And see this FAQ

https://ttlc.intuit.com/community/refunds/help/about-refund-advance/00/27333

You cannot get a loan from TurboTax without your W-2 forms because you cannot file your tax return until you have your W-2s. A Refund Advance is only available when you actually file your tax return in January or the first half of February.

This year (filing 2023 tax returns) a Refund Advance will be one of the options on the screen where you select how you want to receive your refund. You apply for the Refund Advance by selecting that option when you file your tax return. See the following FAQ for more information.

What is Refund Advance?

And…..do not try to prepare a tax return without ALL of your income documents; you must include every 2023 W-2 on the same tax return.  Employers have until the end of January to issue W-2’s.   Wait until you have all of your W-2’s.