How should he go about this?

If child support hasn't been started yet and he wants to pursue legal action this is the time. Your instincts are keen however. He will be fighting an uphill battle. The best course of action he has is to get with a lawyer and begin all the paperwork for establishment of custody. (The lawyer will know what this is) If he has access to the child he needs to get the baby living with him if possible. It helps if he files before she does. It will be expensive but he can win. He will have to pay his own legal expenses. She will be given a lawyer. If he isn't paying child support that will be the first concern of the court. (I do not agree with this but that's how it is). Even if he loses he will get visitation and can have a relationship with his child. Waiting is the worst thing he can do.