The cleverest girl at my school (and she was exceptionally clever) was probably the poorest. And I don't mean playing at poor, either (you know what I mean here: the beat-up Subaru Forrester, the ancient Boden, etc etc), she came from quite a scary council estate.
BUT - her parents were behind her. They worked alongside her at home and helped her until she was helping them. She did very, very well.
You are never, ever going to level the playing field as long as children have different homes. Note - I did not say backgrounds . And, as in my example and in many others "poor" does not preclude success - what does is if your home life is not in any way aspirational.