Contributing to an IRA for the year 2023 after filing your 2023 taxes.

I've already filed my 2023 taxes using TurboTax and received the refund. I made a small contribution to my IRA during 23, converted it to a Roth IRA, and included everything in the tax return.

 

Now, I want to contribute up to the 2023 IRA limit and convert it to a Roth IRA again. The issue is that I've already filed my 2023 taxes.

 

Question: Can I still contribute to the 2023 IRA (non deductible) before the April deadline? If yes, do I need to file a 2023 amendment right away, or can I report it in the 2024 tax year?