how can the father of my child sign his rights away?

You cannot make that decision for your daughter, she is not here yet. Next, father cannot walk away.  Someone has to want to step into his shoes. You could leave him off the birth certificate and never pursue child support. When you need the money, it will be more difficult, but can be done.  But if you wait too long, will get only back four years. You and the baby need the money, are entitled to the money and have a legal right to the money. He does not want to pay?  His problem.