This isn't something that's actually known.
> The differences, if they even exist, are minuscule, while the gender disparity is enormous.
Small differences can dramatically change outcomes.
> It strains credibility to imagine that the root cause of the gender disparity in STEM employment is innate, especially since the disparity varies across cultures and subfields.
"It strains credibility" is another veiled argument from authority. The "root cause" can be different for every culture. Let's imagine that a culture forces STEM to be disproportionately desirable because of societal/economic pressure. It will push more people into the STEM field that wouldn't have joined "naturally".
Then, let's imagine a culture where there are no pressures either way whatsoever. The "innate" differences (if they are allowed to exist) will dominate the outcome completely.
Now let's look at some real-world examples: https://www.theguardian.com/guardian-professional/2015/jun/2...
Would you suspect that more societal pressure (in either direction) is applied in Europe/USA or in China/India/Latin America?