How to send my Daughter to USA to live with her father?

Hello I am a young mother in Cebu. I mistakenly got pregnant by an American man who was vacationing in the Philippines. I now have a daughter who is 3 years old and I am unable to take care of her. Her father is willing to take her and raise her in the USA. I feel this is the best thing to do for her future. He is not on the birth certificate and we have never had any type of relationship. How do I go about getting USA citizenship for my daughter and giving custody to her father so he can take he to live in the USA?

Please no negative responses. Just need help on what I need to do legally. Please be detailed in the steps I need to take.

You can try adoption. That way, you are giving full parental authority of your child to her father.