How can I fight for sole custody of my 4 year old if I can't prove the father is unfit?

I don't think you can fight and expect to win if the child's father isn't abusive or neglectful unless he abandoned the child for a period specified by your state's laws. The only way to get full custody is if the dad signs custody away.

If you are rich enough and can hire enough lawyers and enough PI's almost anything can be done.

But basically if the father is not a danger to the child, he is going to have his rights, and be allowed visitation of the child, this is not only the law but only right if he is the father.

Why do people think that having sole custody of the child is always the answer? Who does this benefit? What is your reason for wanting sole custody?