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There's 150 genes involved in skin colour. How many generations does it take to go from a Nigerian to a Finn if 'some fraction' of the genes are a beneficial change? When you run the numbers it becomes apparent that even explaining human diversity with currently-observed mutation rates is extremely difficult, let alone going from early mammals to humans or even further back to single celled organisms.
Throwing billions of years at a probability with a trillion decimal places in it doesn't help as much as you think. Humans are just bad at large numbers, so it makes it feel more realistic.