Of course there is, just as there was a way for poor rural kids in China to go to the top universities: have public schools offer excellent educations. Pay teachers to offer after-school programs. Pay teachers to give challenging course work. Pay teacher to give timely and frequent feedbacks. It's not about leaving no kids behind, as some kids are simply not good at academics. It's about giving the brights kids, no matter where they come from, a chance to succeed.

BTW, there's nothing secret about Asian students' performance. It's just that even the poor families would know to pool the limited resources to educate their kids.