Well, I have a game like that. I say "like" because it matches everything but the 350 million years thing. I'm not saying my game doesn't do that, I just never knew about the time period of it, so mine may be it.
I have a game for the Dreamcast called Seventh Cross Evolution. You start as a one celled organism and get points to mutate and evolve new body parts. You don't have to unlock them all of course, just something fun to do. It is a life simulater like the another Dreamcast I have called Caution: Seaman, but SCE has stats and fighting, similar to an RPG. Perhaps SCE could be called a life simulator with RPG elements, if you will.
Great game actually. I really connect to those unusual ones. I got my sealed copy just last year and it didn't cost very much at all, so I guess it wasn't too popular. Well anyway, perhaps I shouldn't have rambled on about a game that might be the wrong answer. Maybe I should wait to see if I'm right or wrong next time. Ah well. I'd really dislike to erase all this now...
I'll just wait and see if I got this right. If I did, then that would be very awesome- finally knowing something in this thread without needing to look it up. We shall see though... Later!