Short version? “Show your work.”
Organizations would find it too burdensome if it were mandatory and I suspect that it’d be a political nightmare, mind you. But remember that the point of affirmative action programs is to take, y’know, “affirmative action” to make sure there were no unfair biases in hiring when it comes to historically disadvantaged classes. So, the most straightforward change is to document each step of the hiring process and audit them for conscious and unconscious biases.
That is, the choices of where and how to advertise a job opening, how long applications are reviewed, who interviews which candidates, the explanations for rejecting candidates, and the follow-up (and probably steps in between) are all places where individual companies have identified problems (and publicized them for other people to learn from), and so are reasonable targets to figure out what needs improvement.
After all, you can’t reliably improve a system if you don’t bother to measure anything about it…