My idea:
Campaign part 1
Players are a group of Starfinders investigating the Gap. They get a solid lead on location of archives of some secret organization which was active during that period. They find out that the ancient facility belonged to non other than mythological Pathfinder Society. Moreover they find out that it was an outpost of a group of agents who were pretty active all those years back. Players start to backtrack the way of those agents, visiting different systems and planets to try and get some information on the Gap.
But it seems that somebody made a very good and methodical job of erasing almost all evidence left of the group. And at the same time Starfinders start to feel strange sensations. Places they visit seem familiar though they never been there before. The few clues they manage to find are also strange... And disturbingly familiar. Moreover the methods used to cover the tracks are also very familiar for players!
The climax of the first part of campaign will be players finding an old hologram picture of those old pathfinders presumably being active hundreds of years before. And the moment the players see themselves on that picture I'll give the "session is finished" music...