Competition is generally not a competition in potential skill, but a competition in actual skill.
But we could evaluate potential taking into account youthful disadvantage. Honest accounting for disadvantage would not place the President Obama's children as "disadvantaged" based on being young black women.
You project intent. If the intent was to help actually disadvantaged children to find those with the most potential, class, IQ, parent's educational level, quality of prior schooling, and maybe developmental and nutritional assessments would be the determining factors. As the years went by, genetic testing would probably be added.
Given the low graduation rates of black students in college relative to the rest of the student body, it's untenable to assert that affirmative action is an effective tool for finding students with equal potential "who quickly catch up to the more advantaged students." If you want to target potential by race, there should be affirmative action for asian and white students, who have higher graduation rates.
Competition is generally not a competition in potential skill, but a competition in actual skill.
Here we get back to the point of my first comment.
Suppose that you have two groups, the Blues and the Greens, which have a huge gulf in economic status, but equal intrinsic abilities. Blues are almost all put through excellent, expensive schooling, whereas Greens are haphazardly educated. When they compete for access to higher education, Blues tend to overwhelmingly outperform Greens. Future Greens are left in a disadvantaged position similar to their parent...
Related: Heuristics for Evaluating the Soundness of the Academic Mainstream, Admitting to Bias, The Ideological Turing Test