Cheap and easier access to free online prep courses would help. Also there's a lot that can be done by bringing kids into a community and giving them a group to belong to that encourages education. Freakonomics did a pretty good podcast about a project in Toronto that cut the dropout rate by ~15 percentage points. [0] The whole thing is worth a read but the basics are they provided support advocates, transportation, a scholarship if they kept with the program, tutoring, and group activities.
Really though there's probably always going to be some level of education outcome gap between rich and poor kids, having an easier and more stable home life is a substantial leg up.
Do away with testing [for the purposes of going to Uni] entirely. While you're at it, don't go to Uni either.
The real world doesn't have tests, it has continuous collaboration to solve problems.
This may sound trite but it was my experience and reflects many real-world data points of my friends. Tests and University were a colossal waste of time, and we would mostly be in better positions today [financially, career] if we had done almost anything else with our youth.
I imagine many folks who go to University, wasted their time and public money. There are some whom I would not want to skip that trial however. Medicine, Engineering, Science cannot simply be done by any set of folks in a study group. At some point, somebody in the group has to know what they're talking about.