Given that the X-Men film isn't supposed to come out until after Secret Wars, I bet it'll be similar to how Miles and his family got into 616 in the comics.
The world is "rebooted" (it's the same as before with a few different things), and in the MCU it'll mean the mutants became known to the public in the 60s or somewhen along those lines.
I kinda figured it might be kinda like the end of the Days of Future Past movie. After the multiverse stuff gets resolved at the end of Secret Wars we follow the hero(es) back into the "regular" world, where things are mostly recognizable but we see the changes peppered throughout as a result of the universes merging.
As far as the MCU canon goes the other universe's didn't even
exist until Loki fucked around, right? And then suddenly all these other universes
and their whole histories just popped into being because timey-wimey stuff affects the whole of the past and future? So if the multiverse stuff gets resolved it's possible that rather than "pruning" all the alternate timelines (which the Loki series shows is a damn cruel process) they could end up being blended together into a new "sacred timeline?"
So then the mutants (and probably other things) would have "always" existed in some form in the main canon going forward even if that's something new from the perspective of the 616 heroes we're following (and I hate that they decided the movie universe was
also 616 instead of it simply being treated as yet another universe in the comics continuity). People have pointed out the Fantastic Four reveal image and logo have something of a 60s vibe, so that's possibly gonna be another thing that hasn't happened yet in 616 (ugh) that will have retroactively happened in the new blended universe. Same goes for Wiccan and Speed.
Anyway obviously that's all a big damn maybe but I'm looking forward to seeing where they go with it. Also in general just ready to see the confusing and exhausting Multiverse Saga come to an end. They got what they wanted out of it, they got the previous Spiderman continuities pulled into the MCU for fanservice, they're using it to pull the Fox continuities in, it's served its purpose and I'm so ready to just chill and get back to linear storytelling.
See, the thing I'd hate about this type of twist is that "conveniently" dumping mutants into the MCU in this way, through retcons, is that would kind of undermine what the struggle about being a mutant is all about, and the allegories that have been attributed to them for the longest. It'd be like saying "black/gay/trans/etc. people didn't exist" before a certain era, when they've always been there. I suppose a really inspired team of writers could twist such into an allegory about the "blinders being taken off one's eyes", but I'm not exactly holding my breath for Feige n'em to be THAT on point. LOL
The whole point is that mutants could be anyone. Your neighbor. Your neighbor's kids. Your own kid, or someone else in your family. That dude you sat across on the bus on your commute to work. That nice lady at the coffee shop that always knew how to make your latte the way you liked. That awkward guy you never paid much attention to in your high school English class. Maybe even you, and you just don't realize that truth, yet. Again, I think you really need to keep that, or it just doesn't work as well.
Now, how would I do it?
To me, the answer is simple: When you consider that, in the MCU, very public, out-in-the-open super-heroics is still pretty recent occurrence (2008, when Tony Stark announced himself to the world as Iron Man), it paints a picture that again, mutants could have always been there, but operating in on the low. And certainly in an age before cell phones, it wouldn't take much for powerful psychics on the level of Xavier to keep things quiet, because humanity isn't quite ready for that yet.
Time goes on, and into the modern era. Eventually, even the best laid secrets are going to start getting out, but it's the likes of clandestine organizations such as HYDRA that are scooping up mutants for their pet projects and experiments (which includes, yes, the Maximoff twins, as I assume they'll be retconned to be mutants in the MCU soon enough). Inevitably, these kind of humans rights violations are the kinds of things that well-meaning mutant leadership would love to go to the UN about. Perhaps the likes of Xavier are even encouraged by the likes of the Wakandans revealing themselves to the world, as a similar thing that could be done. After all, they can't hide forever. Nor, as some would attest, should they.
But unfortunately, just like in the comics, Wanda screws up everything for everyone else. The Lagos Incident was bad enough, but at least that was an "accident". Now, we got the Westview incident, too. Suddenly, you got the posterchild of what would easily generate a lot of animosity and hysteria for mutants, everywhere. "You could have a Wanda living next door, and not even know it!" The FOH advertisements write themselves!
And by the time you start having even MORE mutants, in significantly greater numbers, emerge in reaction to the traumatic events that are sure to come because of Secret Wars and the like, there won't be a choice to "hide" any longer.
