What child custody rights does an American man have in Brazil that has a child with a brazilian woman?

The couple has lived together for 10 months and has a child together. They are going to separate and the man needs to move back to the U.S. for work reasons. What reasons would there be for the father to receive custody of the child? Does the mother’s financial situation, mother’s stability, mother’s past(questionable acts), have any bearing on the decision? Also, what governing body makes this type of a decision when there is an American citizen and a Brazilian citizen envolved?

I assume by the question the child was born in Brazil? if so you will need to go threw the Brazilian courts, highly doubt if the mom fights it that Brazil will allow you to take the child to the USA