You can, but not at first. By default, for your first campaign, only 5 of the 21 factions are available. Any playable faction (the Papal States, Mongols, Timurids and Aztecs aren't playable) you destroy becomes unlocked in following campaigns. Winning a campaign unlocks them all. You can edit one of two files in order to unlock them before playing. I did that; I wanted to start as Byzantium.