As an RPG. there is no backstory for the PC because we make it.
Not all RPG. Most of lore-extensive RPG has backstory which tied the character to storyline / world. Even one of the most open-ended RPG game, TES series, offers some kind of background before you starts playing, whether from NPC dialogue / commentary, or simply Race / class description. After which, it depends on Player to build their future lore.
Being the "special ones" or not still asks the question on what does our character even do before we controlled them, that makes them managed to be trusted or powerful enough to carry the burden.
I agree with how psion is a rare trait, and even rarer when random bloke could cast mega strong psionic abilities while in Coma and borderline insane from psycho mania, but still managed to do some conversation. Maybe PC is only normal guy who happens to stumble into SGS and discovered that they have outstanding psi ability (as that SGS doctor guy said). And Tanner, along with that invisible double pyramid faction dudes, guide and used them from behind-the-scene to solves their difficult tasks.
Although this makes PC fate feels like being controlled by the Illuminati lads, which could pull some string to make the PC ends up at such situation. Also, it's kinda weird that super secret agent Abram just chilling on literal dump town and just give very important tasks to random guy he just met.
Maybe they even controls the flow of Faceless by "accidentally" lose the Thing and stir-up Core city for their secret objectives