Can the court make someone be involved or pay for a child that not be theres? He's not even on the birth certificate.

My boyfriends ex recently just had a baby that she's been claiming is his from the first month BUT she told us it could be someone else's as well. Once the baby was born nobody but her and her family said it looked like him. He's not a birth certificate and he hasnt been involved which is why she's going through the general attorney. Can the court force him to drive over an hour to see a baby that may not be his, or Pay for a child that may be his? Does he have to pay for the DNA test? Would I be allowed to go since were due to get married and I'm pregnant? Would the baby get to come home to us if it is his? She tells us all the time the baby will never come home with us as long as she has a say in it. We both have a house, vehicles and steady jobs.