If the woman has custody of the child..the fathers name is not on the birth certificate?

the father cannot uphold his financial responsibiltys beacuse of his other kids,bills etc so now he has to move in with the latest baby mamma #5 to keep his head above water... should he be able to keep the child that we made and introduce him to his new family or should i wait until i know he is settled with this new family.I have a stable place to stay and I work FT to pay all my bills ALONE and take care of my 3 kids..ALL BY MYSELF