How long do I have to wait with no contact from my child’s father to file abandonment on him?

Yo can not get his rights. If he is not on the child's birth certificate, he has no rights. If he is on the certificate, the only way to terminate his rights is by adoption. You can not file abandonment anything. His lack of interest may be a basis for denial of visitation if none is ordered. If he is not seeing the child and there is no court ordered visitation, just keep a diary for use at a later date.