How long did it take nature to go from T-Rex to chickens?
There’s no reason to believe human level intelligence to be an inevitable result of evolution. It just happend.
Not that I agree with the sentiment in the GP, but it took a relatively short time from the first development of multicellular life until nervous systems developed and an even shorter amount of time to go from small mammal intelligence to human intelligence. However, evolution isn't about "progress" as we understand it. The most we can say with regards to intelligence and evolution is that human intelligence satisfied a niche that existed at a certain place and time.
So I think the estimate of 3-5 years might be realistic, but the artificial mouse is a long way away, IMO.
I'm not sure creating an intelligence that even supercedes our own will lead to anything good. If anything I'd expect things to get even more perverse.
But how long did it take Nature to get from a mammal with mouse-level intelligence to a human-level brain. I think 200-ish million years [0].
You might be right that a mouse is a good indicator of high-level intelligence and that you don't need human-level intelligence to make a good AI, but there might still be some considerable way to go until we have an AI that can significantly outperform us.
[Edit - I agree that natural selection wasn't aiming or directed, and thus wasn't forced to be as fast as we could be. But a human's higher brain functions might not be simple incremental improvements over a mouse's, and there could still be a long way to go]
[0] https://en.wikipedia.org/wiki/Mammal