There's a lot of bad "colorblindness" advice in this thread being met (rightly) with refutation, but no one here has really answered OP's question. When we talk about racial and gender inequality in the workplace, we're talking more about observable systemic patterns of oppression and ignorance than individual hypothetical situations. (On that note, hypothetical questions and situations are useless, and possibly toxic, in social justice circles, but let's humor OP.)

Workplace inequality manifests itself in many ways, including (but not limited to) pay gaps, harassment, and (ahem, OP) hiring practices. The latter of these effects refers specifically to a consistent pattern among job recruiters whose hire selections are overwhelmingly white and/or male, though the entire hiring pool isn't as monochromatic as these hires indicate. The problem isn't just hiring one/some white men, period; it's that hiring a disproportionate number of white men when compared to the available job candidates is indicative of unfair hiring practices. You can hire some white people and/or men, but hiring only or mostly white people and/or men is unjust and oppressive, especially when those hired either have the same or lesser qualifications than applicants who are women and/or PoC. (This is a very common phenomenon as well.)

Racists often use "I hire those who are best for the job!" as an excuse for consistently making monochromatic hires. The problem with this is that they're not telling the truth: They don't actually hire the best people for the job. If you, OP, are genuinely looking for the best-qualified candidates for the positions you're in charge of filling, the group of people whose qualifications truly merit consideration is certainly not going to be monochromatic. There's no way that the best-qualified person for every position just happens to be a white man; there are too many different careers to be good at for every single field/job position to be dominated by white men by any virtue beyond privilege. A specific white man might be the best-qualified candidate for a specific position at a specific company at a specific time, but that's a hypothetical individual situation that needs to be judged appropriately in light of racism/sexism, i.e. documented and pervasive social phenomena. That ideal hiring round of qualified candidates we're (ugh, hypothetically) assembling may well include some white men, but it won't be exclusively or mostly white men.

(Further, if your workplace is exclusively or mostly made up of white people and/or men, it might be time to reevaluate who the company hires, but that's not a general rule for hiring so much as it is a deliberate counter-measure to a specific, albeit disturbingly common, situation in a given workplace. Also, be careful of tokenism if this is necessary: One or two PoC employees in an office with dozens of white employees doesn't make a workplace diverse, for example.)

Because of your privilege you'll need to think critically about the candidates you ultimately decide to call back for interviews, and there are a lot of supposedly "significant" factors that are commonly thrown around in hiring situations which are realistically irrelevant or tremendously unfair to judge (e.g. what college someone attended, previous workplace experience, etc.). Being empathetic and allowing equity for minority candidates requires that you actively do this as you evaluate all your potential job candidates. This requires a degree of diligence and detachment from personal identifiers, and a willingness to make room for differences in the workplace. It's not about colorblindness or directly "combating privilege," it's about cutting some slack for people who need it and looking for those who are qualified when privilege is (at least somewhat) accounted for.

When it comes to specific positions and interviews... Well, frankly OP, you're on your own there. No amount of hypothetical thought experiments beyond being conscious of privilege and deliberate empathy toward potential hires from a minority will give you a clear-cut set of rules for socially just hiring. Again, if you actually hire the best-qualified candidates for a hiring round, the group of people you hire is, by the virtue of being critically assembled (i.e. by you checking your privilege) and equitable to the circumstances of minorities, is going to be diverse and (at least generally) representative of society as a whole.

TL;DR: Check your privilege, think critically about hiring criteria, and do this in the context of deliberately looking for the best-qualified job candidates. Avoid colorblindness and be empathetic about minority struggles, but don't treat minority interviewees like special tokens. Doing this correctly would (again hypothetically) result in a group of hires which is truly representative of society's diversity: Some of this group will be white, some will be PoC, some will be women, some will be men, some will be trans, etc., but a realistic group of the best-qualified candidates will never significantly favor one particular demographic over another.

Still TL;DR: Check privilege. Be careful about evaluation criteria. Watch out for patterns in hiring practices. Don't treat minorities like token hires. Hire groups of people which reflect the diverse makeup of society, because chances are those representative groups will be closer to a "meritocracy" than any homogenous group could possibly be.

Edit: Clarity and grammar.