He CAN TRY. In order for him to try, he will have to establish paternity (which it isn't clear if that was done), there will be a parenting plan, there will be a child support plan, and THEN he MAY be able to stop you from moving out of state. In the meantime, if he has not taken any of these steps you can move out of state.
If you up and move, he is going to have to sue you in your new home. Now to be fair to your child, even if you successfully move you need to make arrangements for your children to see their father. You should not let him have the children without a court ordered parenting plan.
Many around here will disagree with my advice. Ethically you SHOULD get a parenting plan, and he CAN try to get you to stay in the state. But you are under no obligation to do so right now and if you move before he files anything then the court is unlikely to order you to move back. Now there is the possibility the court will order you to pay the costs of travel for visits when they are ordered.
Happy Thanksgiving. I charge double for advice on holidays (Free Free).