Honestly, a way I can see X-Men intergrated, is from aftereffects from the battles of Infinity War (and presumably Infinity Gauntlet) causing people all around the world to start getting mutations, and with government programs starting up to prevent if the Avengers turns.
It could then lead the way to Origins for Wolverine, Mystique, Professor X and Magneto and more mutants with more possible ease, with it being different than the Singer/Fox X-Men universes.