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There are never 100% guarantees when it comes to court cases but from a practical standpoint I see no reason you would not be awarded full custody. If there are no court orders in effect you need to be careful allowing the father to take your child alone since if he kept the child you would have no court order to get the child returned. You need to file a motion for custody in the family law court and get a court order for custody. The father will be entitled to some visitation depending on the circumstances and he will also be ordered to pay child support. I am assuming you are not married to the father.
The court determines custody based on the best interests of the child and there would be no court I know of that would give custody to a father who has not been involved in his child's life.