If the mother is OK with me singing my rights over and there is no one to adopt, will the state still let me ?

You cannot sign over your rights - https://www.askmehelpdesk.com/family-law/signing-over-rights-read-first-116098.html.

This is asked (minimally) on a weekly basis. You will be responsible for child support until the State allows you to relinquish your rights. Of course, the mother does not have to pursue you. If she is getting benefits, the State can pursue you.

But, in a word, no.

Why the hell do guys think they can just walk away from their child because they don't get along with the mother anymore?

GROW UP AND STEP UP.

That kid NEEDS you to be a dad, and to provide child support.

The mother was good enough to have sex with, now she ought to be good enough to get along with for the next 20 years or so while you raise a child together.

Next time, if you don't want a 20 year relationship with a woman, and don't want the responsibility of a child, take the time to catch your penis in your zipper so that you don't have sex with her.