Is there a way to prove my baby's daddy is not a good father figure?

To who ? And most "baby daddy" are not good father figures, since they are not a father, living at home with the child, or not including the child in their lives if not living at home with them.

But that has nothing to do with anything, if he wants court ordered visits with the child, what you have to prove is that he is a danger to the child, not just a bad role model