Proof for what? Smaller number of available women? That's obvious. That if larger companies hire the best of them, the remaining supply/quality will shrink? That's obvious too.

No, that there's a hard number that Google recruiters are supposed to achieve (50% seems to what I've seen repeated around here.)

Does anyone have any actual proof that Google is aiming for 50% or to represent the general population 1-1?

It sounds like they kept meetings deliberately off-the-record, but then again here on https://www.google.com/diversity/index.html there's stuff like "we’re committed to making our workforce more reflective of the world we live in". Number goals are unlikely to be published for obvious liability reasons.