Can I get visitation or custody, even though I was not married to the mother, and I am not on the birth certificate?
A father can always get time-sharing with their child, even if they’re not married or on the birth certificate. That can be done through the initiation of a paternity action. The paternity action will establish you as the father of the child. You’ll be placed on the birth certificate at that point. You’ll have time-sharing rights, parental responsibility.
Obligations regarding child support could go towards the father or the mother, depending upon the results of the child support calculations. By initiating a paternity action that results in you being named the father, you are that child’s father for life.