Its always a good idea to browse around a bit and look for similar threads before posting your question. Had you done so you might have seen this sticky:
https://www.askmehelpdesk.com/family...st-116098.html
You would have then learned that your son can't just give up his rights. The child's mother can and should file for child support. If the mother needs to apply for public assistance the state will, almost certainly, require that he pay.
Your son needs to plan on dealing with his decision to engage in sex with the girl and his responsibilities to his child.