If custody has not been established, can a parent legally move their child out of state?

Lets say the father of a child has abandoned his child and girlfriend, is unable to be found, and has not provided any type of financial support. Lets also say there is currently a warrant out for his arrest due to a domestic violence charge and threatening the life of his girlfriend and child. There is also an order of protection against him. If the mother wants to move out of state and take her child, of which she’s had in her care from the day of birth and since the father left, is she able to legally do so without the consent of the father? If not, what would the proper steps be? This is in the state of NY.