Statistics can be useful but they aren't 100% proof of anything. The gender pay gap fails to take into account a multitude of factors - age, experience, qualification, track record, and of course luck. There may also be other factors in individual cases.

Statistics are literal 100% proof of a great many things. That’s why they are statistics not just a guess.

The whole point of them in this case is that they support exactly the point of your argument.

In order to work out why women aren’t getting into top jobs odd necessary to establish that it is in fact the case that they aren’t.

All your points are what follows - why aren’t they. The answer could be any one of the things you list on an individual basis.

But more potently one of those reasons may not be as uncontrollable as luck.