Actually, i think Using Magneto, in this case, right out of the gate, is the CORRECT choice. Just say mutants have always been there, just really, REALLY rare. Say that quicksilver and Scarlet witch WERE mutants who were being experimented on, not the result of experiments, that's just what they were told.
Go for it, and make the first issue of X-men, where magneto has had it with being in the shadows, and makes a dramatic public appearance, announces their presence, and attacks a military base.
Why has no one learned of them before now? Xavier has been erasing people's minds for YEARS. but this time, Eric was too bold, and there is NO putting that genie back into the bottle. ON TOP OF THAT, Mutants are starting to be born more often. why? perhaps it has omething to do with the infinity stones, who knows. whole plot of the movies there could be WHY are mutants popping up so much more frequently.
People of earth are starting to kinda trust heroes, but now, mutants come out of nowhere and attack? you want a reason to turn, and hate and fear? there it is.