My point is that we could NOT have evolved into our current state in the
time available.

Sadly, all evidence points to exactly that. Your problem is the timeline, based
on VERY limited data on evolution.
What you fail to release is that evolution has probably slowed due to a general
geological stabilization over millions of years. It MAY have moved at a faster
rate and all indications are this is exactly what happened.
No big bearded gods need apply.

RB