Paternity, Custody. Oklahoma Is there a way to establish paternity without going to court if mom won't cooperate? Father's name on birth certificate?

My son is in the military. After deployment, he met a woman in a bar. He did not know she was married. She referred to her husband as her ex. She became pregnant said baby is my sons. He moved her into his house along with her older child. My sons name is on the birth certificate of the baby. Fast forward two years. She is still married to the other man. Her husband has initiated divorce proceedings. The baby is not mentioned in the divorce. My son is "done" with the relationship with the mother and wants custody of the baby. Son has been transferred to another State, but mother and child are in OK. My son has provided full support for the mother, baby and older child for almost two years. My son was told that having his name on the birth certificate does not entitle him to parental rights. He was told he would need to win a paternity suit before he could file a custody suit. No DNA testing has been done. Mother seeking welfare, will welfare dept require paternity?