you could run a female cohort that is subject to nonstop social encouragement "you are powerful. you belong." and then observe whether they reach the same levels of achievement. If they do not, then this is evidence that the achievement is not due to social encouragement.

You could alternatively look at the negative manifestations of variability, like increase crime and violence, and try to socially discourage it. Expose males to "crime is bad. bad men go to prison where they cannot have sex with women for many years. if you do crime you are bad." Observe whether crime rate of men relative to women decreases. If it does not, it is evidence that social encouragement is not responsible for the difference in crime.

You could also do a control where you discouraged men from achieving. "Nerds are gross" and see if that leads to a victory for feminism.