It looks like you can choose almost any civ you want if you can meet the required criteria.
From the hints and glimpses, it appears that you have a "historical" progression based on the Civ choice (the much-discussed Egypt to Abbasid, or Rome to Norman), But you also have other choices based on your Civ or Leader or some other criteria.
For instance, the criteria for choosing Mongolia in Exploration Age so far is only given as "Requires 3 Horse Resources". Unless they are hiding something, that means Egypt, Maurya, Greece or Rome could become Mongolia if any of them have 3 Horse resources.
The AI may be programmed to make a First Choice of the 'historical' progression, but Human gamers aren't.
And (and I would be very surprised if they haven't already thought of this) they could open up the choices even more if the 'Historical" progressions also had another Unlock Condition. For instance, if Egypt does not choose Abbasid, someone else who had chosen a certain Religious Pantheon or combination of Religious/Social Policy could choose it.
That, of course, runs the risk of falling into the Humankind Trap where choices are so potentially wide that it becomes confusing, but having limited the system to only two choices (Exploration and Modern Ages) I think that is a risk worth taking.