I still managed a pickup of Islam in 500BC... of course, it was made easier to access.
BTW, 5 mujahids at that point in the game, where my best unit was a Nordic Warband or Mounted Warrior, I think it's too much for something you get purely from tech. A lot of AIs were still using the first archer class, and armies were not too strong.
I've generally teched fast (monarch difficulty) when the game is right. The problem is Pastoral Nomadism is way too good, especially on America. Either the Ranch needs to be nerfed, or Pastoral Nomadism in general should be nerfed, probably with -50% GPP so you don't have nomadic steppe philosophers teching hard before the Greeks became a thing. Alternatively, a hit to research - maybe -10-20% - would balance it. I can tell from the presence of cows in my capital whether I'm going to do well or not. I see Pastoral Nomadism as a way to play a light development strategy to get a lot of settlements up quickly, either for a war machine or for passive expansion, but it needs to be punishing on research so that it's not an automatic decision. I don't know the AI's exact behavior regarding that civic.