First off, I don’t really want to put the X-men into an entirely different universe as that may diminish what makes the MCU so special.
In the Marvel Cinematic Universe, many people posses the X-Gene but some Mutant Abilities can only be unlocked by a mass amount of energy. Wanda Maximoff and Pietro Maximoff will have possessed that gene and gained their abilities from the energy radiating from the Mind Stone. Magneto would’ve gained his powers from the Tesseract, which was in the hands of Germany during WW2 and most likely where young Erik would have been. Some Mutants receive their powers naturally whenever they become teenagers like Jean Grey, Scott Summers, Hank Mcoy, Warren Worthington, and Storm. These teens operated within a government-funded covert squadron in the early 2000s called the “X-Men” under Charles Xavier. The group disbanded after a mission resulted in a massive amount of Collateral Damage and Warren (Angel) was severely injured. Charles Xavier erased the minds of anyone who had come in contact with the team and retired in upstate New York to open a school for “gifted youngsters”. Fast forward to when Thanos snapped his fingers and a massive amount of energy caused children all over the world like Kurt Wagner, Kitty Pryde, and Victor Rasputin to gain Mutant Abilities. Eventually, the old team (excluding Angel) re-unite and help train a new generation of Mutants but must also defeat a S.W.O.R.D geneticist by the name of Nathaniel Essex (Mister Sinister) who is taking advantage of the recent Mutant boom to benefit his own devious plan. Eventually, Rogue, Gambit, Wolverine, and Magneto would be introduced into the MCU in a potential sequel.