Legal Question in Family Law in Texas

What is most likely to happen is that you will both be named joint managing custodians of the child but the child will be placed in your care & he will probably - very probably - get only supervised visits until she is older and he takes a parenting class.

You should take the initiative to file and get orders. As it stands, if he took the baby from you physically, he could do so because it is his child, too, and there are no court orders.