What are my sons rights now, at birth, and after? He has none. Until after paternity has been established by the court, he has no rights at all.
Does he have to wait to prove paternity if they are uncooperative? Yes. He would have to wait to prove paternity even if they were cooperative.
If so how does he do that when he won't even know when baby is born? He can put his name on Ohio's Putative Father's Registry.
ODJFS Online | Putative Father Registry
Do not even imagine that he will get 50/50 custody. He may get joint custody but it won't be 50/50 physical custody. That's simply not going to happen.