As of the game opening, there are no Factions beyond SHIELD, Checkmate, the Green Lantern Corps, and the Xavier's Institute. Xavier's does not have any sort of X-Men/etc team. It is simply a safe haven where metahumans learn to use their powers. There is history of some minor super teams in recent IC memory, but there are currently none, and there has never been one on the scale of the Justice League or Avengers.
The formation of any such team, or a group similar to the X-Men is entirely up to the players to do as they will, though staff will help facilitate as needed. If Jubilee, Blindfold, Noriko, Karma, and X-23 are the people who start the X-Men, they will historically be the first X-Men. Assuming they even call themselves the X-Men.
What is a Mutant?
What is a Metahuman?
SHIELD
Checkmate
Crime