You can't control for the social conditioning of gender. This is so fundamentally obvious I don't think you are taking the science seriously.
When the data consistently shows gaps widening as social strictures loosen, and your response is to blame an invisible, unmeasurable "conditioning," you aren't doing science at all. But you are insulating your belief from any possible counter-evidence.
Note that this outcome goes both ways. We can neither confirm that biology is the main driver nor confirm that it isn't. Life is not as certain as you want it to be.
All of the evidence is solidly on one side, so you’ve retreated to “we can neither confirm nor deny.”
I guess that’s progress?