The X-Men would never have fit in Phase 1 of the not the Quicksilver in X-Men.
The X-Men were originally owned by 21st Century Fox, so Disney, and Marvel, did not have the rights to the X-Men until they acquired 21st Century Fox in 2019. Fox built their own world for the X-Men, which led to spin-off films such as The New Mutants. Throughout the X-Men universe, Charles Xavier's team often fought to protect themselves as mutants and stay hidden until they could live peacefully alongside humans in a future that never materialized for the X-Men.
Phase 4 is massively expanding the MCU, and the introduction of the Multiverse gives far more possibilities for introducing the X-Men as a result. The MCU's Phase 1 was primarily Earth-based, with the only appearance of Avengers. Although the mutants could have still been introduced in Phase 1, it is unlikely that they would’ve been accepted without having their own war with the humans instead of fighting with them against other forces. The X-Men films frequently show how mutants threaten humans instead of feeling protected by them, even when fighting on the same side - making their highly anticipated Phase 4 appearance a far more natural choice for the X-Men's MCU introduction.
In this way, the Multiverse expansion is the perfect opportunity for mutants to be introduced into the MCU. New Marvel movies such as Eternals show that the X-Men could have existed outside of human knowledge up to this point, whilst the Multiverse also shows how many possible alternate timelines and different ways there are to explain the X-Men's sudden appearance. Also, post-Avengers: Endgame, the status of the Avengers and their current mission has been less clear. Although the initiative is still running the MCU, there is currently no clear team and a particular lack of Earth-based Avengers. Many of them fight in other areas of the galaxy, such as Captain Marvel (Brie Larson), or are presently stuck dealing with the problems and threats in their own lives, such as Wanda Maximoff (Elizabeth Olsen).
This lack of stability for an Earth-based Avengers team, therefore, provides the perfect opportunity for Marvel to introduce the X-Men and rebuild the Avengers, making them a focal point of the MCU. Spider-Man is also a mutated human, making phases 4 and 5 the perfect time to introduce mutants as the science is now already part of the MCU. The X-Men are humans with a mutated X-gene, so Earth is their home, and they are likely to fight for it, making them the perfect option for the new Earth-based team. Trying to fit them into the restricted Marvel Cinematic Universe Phase 1 would have been problematic, but Phase 4's introduction of the X-Men represents the perfect opportunity to integrate these iconic mutants into the MCU.
