You could compare different societies, for example Saudi Arabia and Sweden. If some gender differences remain, it is still not certainty, but it is quite likely

You could compare different societies, for example Saudi Arabia and Sweden. If some gender differences remain, it is still not certainty, but it is quite likely that they are caused by some brain chemistry. (Unless you believe that Sweden is just as patriarchal as Saudi Arabia, in which case I guess there is no argument that could possibly convince you.) Another possible approach is to examine what happens to transgender people after they start taking hormones.