With the FF, it would be kind of easy to just say, "They went into space in 2008 in order to beat the Russians and the Chinese to a space anomaly on the far side of the moon of Titan. Now they're back, with strange powers..."
But how would you introduce the X-Men? I was thinking that before the snap, mutants were highly unusual. You pretty much had Magneto and Xavier and they kept themselves hidden. After the snap, kids started developing super powers as a result of the "snap." Along with kids developing powers also comes this distrust by parents and people in authority who had created heroes.
Xavier forms a rescue squad to find mutants and help them. Magneto forms his Brotherhood, as a sort of mutant supremacist movement.
After the snap, the universe is different. The MCU history you thought you knew is wrong. Superhumans aren't some new or rare concept-- they have always been around. 'Nuff said.