We don't need to wait for genetic data mining, this has been widely studied already.

Differences are visible within the first two days of birth : https://www.researchgate.net/publication/222673203_Sex_Diffe...

and are present in monkeys too : https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2583786/

I'll let you draw the conclusion.

Table 2: Mean percent looking times (and standard deviation) for each stimulus.

                          Face                    Mobile
    Males (n = 44)      45.6 (23.5)             51.9 (23.3)
    Females (n = 58)    49.4 (20.8)             40.6 (25.0)

That's quite a difference to be hanging the nature of society on.

Yes but to speculate that a baby's desire to look at a face more means they're less able to negotiate their pay is a bit of a leap (as opposed to that being social or cultural). Sure there are literal differences between gender but one still has to ask that if those differences are big enough to make a difference following the YEARS of nurture or not.

I'll wait till the genetic data mining transitions this from speculation to fact thank you very much.