The study examined female and male brains, found that males on average had a higher general intelligence score and a higher standard deviation. The study also found that male brains had on average higher surface area and size even if you control for body size. The study found that brain size in both genders on average leads to a higher g.

I don't understand how your criticism "indirect correlational evidence" applies to this study, could you maybe elaborate on how you would improve this study?

Well hell, the Newtonian laws of motion had no hypothetical mechanism for gravity for a rather long time. We're still in the early days of figuring out Homo sapiens. Don't get your knickers in a bunch, yet. It looks like you're uptight about something.