The way I would go is establish that there have been mutants all along, but in very small numbers. Say, one in every hundred million. Establish the x-gene as something that is actually present in large portions of the population, but it just needs to be activated somehow.
Flash forward to the snap. As Rocket said, the entire planet was awash with strange energies that nobody had ever seen before. We know that infinity stone energy gave powers to Carol danvers, Wanda and Pietro maximoff and Monica Rambeau.
The Xavier and Magneto of this time line are pre-snap mutants. Also, Wolverine, but I'll get to him in a bit. Xavier and Magneto managed to find each other and strike up a friendship with many theoretical discussions about an expanding mutant population. Now that that's actually happening, the discussions turn into arguments and we all know where the arguments will lead...
That said, I would want the MCU X-Men movies to be about the students, rather than the Xavier Magneto conflict because that's all that FOX focused on. For that matter, I wouldn't even include Wolverine in the X-Men... At first.
I would have two concurrent movie trilogies, one focused on the X-Men, and one focused on Wolverine through the years. The third X-Men movie in the trilogy would end with Wolverine joining the X-Men.
Anyway, that's what I would do.