Father of child not on birth certificate?

bianca
Ok so I'm posting this for my friend. She had her daughter back in July. The deadbeat baby daddy is MIA. She isn't working because she can't afford daycare. Her brother and mom are helping her out as of right now. She is in school with 1 semester left and paying out of pocket. Now she is finally considering putting the deadbeat on child support. She just told me how the baby daddy isn't listed on the birth certificate, but it is his. Will this make her case difficult against him? He already has a kid, but he is a bum and will do something petty by saying it isn't his. Btw she gave her daughter her last name too.
Sorry I didn't know where to put this at.