It's possible, yes. It's also possible that perceptions of race influence the subjective decisions that drive those outcomes. How would you determine causality?
Eg, you could try sending employers identical resumes with "black sounding" and "white sounding" names and measuring callback rates. This has been done: https://www.politifact.com/punditfact/statements/2015/mar/15...).
There are likely many factors in racial disparities, but this appears to be one of them.
https://www.chicagotribune.com/business/ct-bias-hiring-0504-...
TL;DR: Original study used names that coded for socioeconomic status as well as race, and is older so people may have been more racist then than they are today. Newer study using names that ostensibly code for race and gender but not socioeconomic status shows no difference between race or gender coded names.
Sure, possible, in the sense of theoretically possible. But very unlikely as socioeconomic factors potentially dwarf all of the aggregate group differences.
Not only that, people want to continue using the existing (extremely flawed) categories, and that's where it leads you to problems.
"More genetic variety in a single race than between races" is a great argument for why you shouldn't discriminate based on race -- even if the mean for some "race" is higher or lower, that doesn't tell you much about the individual before you.
But it does tell you something about aggregate statistics. When you discover that some "race" is underrepresented in some field, it's completely possible that a major cause is that the median in that arbitrarily defined racial category is below the median in another arbitrarily defined racial category. Which can be true even when a significant minority in the worse off racial category is above the median in the better off racial category -- which minority constitute most of the people of that "race" who are represented in that field.
Ideally the solution is to recognize "race" as a garbage category with no scientific basis and stop using it for anything, ever again. But that is where politics gets in the way, because people have built their political coalitions around the flawed concept that categorization based on race is anything more than an error.