Heard rumors, though all of it is blantant speculation, that maybe they’ll use the ‘snap’ or the undoing of the snap, to trigger the mostly dormant ‘x-gene’ to get mutants. So maybe before the snap there were mutants but very, very few of them, so any mutant power stuff were strange isolated incidents that were random and unexplained (or explained as something else.)
The only x-characters that need to be ‘old’ and have history or Xavier wolverine and magneto. Xavier and wolverine, it would be easy to believe they were just laying low, living their lives, helping occasionally when they could but alone couldn’t do much. Like if wolverine’s in the army in Afghanistan when New York is attacked, he can’t get there to help in time. And all of their powers are nerfed at the time (which would explain magneto laying low, he can’t attack army bases by himself, he has to be more subtle.)
Gambit could still be street kid, ends up with the guilds (which would be more a gang/ crime syndicate) maybe he still has the black eyes but no powers, so his still kinda freaky/outsider but relies on his thief skills. After the snap, he gets his powers ( maybe that’s how he accidentally kills julien and ends up leaving New Orleans) So the snap triggers a bunch of mutants (exististing mutants get a boost of some kind). Gambit’s flexible enough that he could start out on the X-men or as a free agent or even the brotherhood and switch. Sinister could also be a pre existing mutant, so he could recruit gambit too.
Either way, first movie should start a few months or maybe year after the snap, so mutants have been popping up, the general public is freaking out over the wierd-ness, the avengers are trying to get a handle on the whole situation (but they don’t really know what’s happing and Xavier has started his secret school/sanutary.) The new mutants (;p) don’t have to be all kids/teenagers, it will settle down into that eventually but the initial snap would jump start adults as well.
Anyway that is my rambling, probably wrong speculation, lol.