Then anonymize the resumes so that recruiters can't tell which candidates are men or women, or which is white, Asian, Black, etc. You don't eliminate discrimination by setting caps on how many interviewees can belong to each race. It certainly could be the case that whites are advantaged (curious why you focus on whites despite Asians being far more overrepresented, by the way). Put the proverbial veil between the candidate and the hiring manager, and we'll find out the truth.
One of my previous workplaces rejected proposals to anonymize our interview process, on the grounds that it would inhibit our diversity initiatives. Interviewing.io did an experiment relative to gender with anonymized phone interviews, and the result were the opposite of the traditional narrative [1].
1. https://blog.interviewing.io/we-built-voice-modulation-to-ma...