It depends on whether the parents married

If the parents  are married, then the parties have equal rights to custody until a court order is put in place. If the parents are not married, then the mother has the custody of the child until a court order is put in place.

There is no legal presumption of paternity. This means that a man is not automatically assumed to be biological father of the child. If the father desires to have custody, he must first establish paternity. It can be done by the man voluntarily accepting paternity.

On the other hand, if the mother does not agree the man is the biological father, the man must submit himself to a DNA test to establish paternity. Once paternity has been established, the father can petition the court for a custody order.