If parents agree that one parent should have sole legal and physical custody can a parent file for child support

Any agreement made can and likely would be changed by the court because the parent paying the support can easily decide they want full or partial custody... after they realize they are paying the bills.

SO anything you two agree on outside the courtroom isn't really worht the paper it would be printed on... because it would be unenforcible... unlike the court orderd one. And a smart set of parents would do it through the court.

Maybe an agreement drawn up by an attorney would have some weight, but its unlikely.

Best to go to court and make everything official.

But, if one parent is giving sole legal and physical custody, the other usually pays support.

Yes a parent of a child or children can apply for support at anytime provided they are following the laws of the State they reside in.