My girlfriend left me & moved out of state with our daughter what now?

Unmarried Parents
When a child's parents are unmarried, the statutes of most states require that the mother be awarded sole physical custody unless the father takes action to be awarded custody. An unwed father often cannot win custody over a mother who is a good parent, but he can take steps to secure some form of custody and visitation rights.

For unmarried parents involved in a custody dispute, options for the custody decision are largely the same as those for divorcing couples -- child custody and visitation will be resolved either through agreement between the child's parents, or by a family court judge's decision. But, unlike divorcing couples, unmarried parents will not need to resolve any potentially complicated (and contentious) divorce-related issues such as division of property and payment of spousal support, so the decision-making process is focused almost exclusively on child custody. For this reason, resolution of custody and visitation may be more simplified for unmarried parents.

If unmarried parents do not reach a child custody and visitation agreement out-of-court, the matter will go before a family court judge for resolution.
You can file for visitation to see your child if you on the childs birth certificate, if not you will need to take a partenty test to establish if the baby is yours, before filing a motion with the court, if your girlfriend left state, she will not be able to file for custody until she is a resident of the state she moved to, although I have seen where parentsfile for custody, and get it, because the court is not aware that they are not a resident. You might want to contact the mother and see if she will agree to joint custody, and give you visitations, you both can file a motion and the court will grant your wishes if you file and agree.