I messed up on my 2020 tax return and didn't receive the 3rd stimulus. If I amend it, will I receive it?

I filed my 2020 tax return earlier this month and already received my return. However, on my return, I accidentally said that I was able to be claimed as a dependent by someone else when I meant to say no. This made me ineligible for the 3rd stimulus. If I amend my return once the 1040x is available, would I still be able to receive the stimulus or would I have to wait until next year to claim it as a rebate when filing taxes? Thanks.