If the Fantastic Four were to be introduced, I think the only real way to do it would be through a television show. Taking some good points that posters have mentioned earlier, Reed could have been an established scientist working with an organization unrelated to Stark Industries or SHIELD, something plausible if he was working on dimensional/space travel unrelated to weapons and such. This would allow for him to be well-established and famous in universe while not having been seen thus far. Sue could be working with him and Johnny could be a celebrity in his own right.
Events from the MCU could have inspired him to feel the need to push his research forward quickly, ignoring protocols and such leading to the origin of the team's powers.
The television series format would allow sufficient screen time for the FF to become the prominent figures in-universe between movies. Although it probably won't allow time for a full solo movie during the show's run, the team could certainly appear in the movies as well-established characters, both in universe and to the audience.
Events from the MCU could have inspired him to feel the need to push his research forward quickly, ignoring protocols and such leading to the origin of the team's powers.
The television series format would allow sufficient screen time for the FF to become the prominent figures in-universe between movies. Although it probably won't allow time for a full solo movie during the show's run, the team could certainly appear in the movies as well-established characters, both in universe and to the audience.