No taxes filed in 2023. How do I authenticate with the IRS for no AGI and Reject Code IND-031-04?

If using 0 doesn't work you will have to print and mail your return.  Try entering 0 for the AGI. The IRS might have processed your return later so the AGI didn't get entered in time.  Especially if you mailed it.  That works for most people. See,
https://ttlc.intuit.com/community/rejections/help/what-if-i-entered-the-correct-agi-and-i-m-still-getting-an-e-file-reject/00/27031

How to correct the AGI in the Online version
https://ttlc.intuit.com/community/agi/help/where-do-i-correct-my-agi-in-turbotax-online/00/26311

If you can’t get it to efile you will have to print and mail it.
https://ttlc.intuit.com/community/printing/help/how-do-i-print-and-mail-my-return-in-turbotax-online/00/26258

Be sure to attach copies of your W2s and any 1099s that have withholding on them.  You have to mail federal and state in separate envelopes because they go to different places.  Get a tracking number from the post office when you mail them for proof of filing.

If you did not file a 2023 tax return, you can choose the answer that says you did not file for 2023, or you can try using zero.   If neither of those attempts work and you still cannot e-file, the remedy is to print, sign and mail your tax return.

When you mail a tax return, you need to attach any documents showing tax withheld, such as your W-2’s or any 1099’s.  Use a mailing service that will track it, such as certified mail so you will know the IRS/state received the return.

Federal and state returns must be in separate envelopes and they are mailed to different addresses.  Read the mailing instructions that print with your tax return carefully so you mail them to the right addresses.