So when Starfinder had been announced but before it came out, I misread a spoiler/summary about the timeline of the game. I thought that the Drift Drive was almost a "brand new" device in the hands of Pact Worlds and - as such - there was a kind of a land rush on to find new worlds with the Drift Drive. I found this to be a compelling basis for the story, and fitting in with trying to find information to fill in the Gap.
That isn't the official timeline, of course. But I've been pushing that kind of setting back and forth in my head, and I was thinking about this article from The Alexandrian.
http://thealexandrian.net/wordpress/36890/roleplaying-games/random-gm-tip-r ewind-your-timeline-how-to-use-published-sourcebooks
I like the idea of the Drift having opened up only three years prior, and now the Pact Worlds have gotten a whole lot smaller. Absalom Station's beacon is bringing all sorts of crazy things in from the far reaches of space. There's a huge number of worlds to explore (including many of the snippets on worlds in published materials).
Alternatively, you could wind back individual locations in the Drift being discovered, and have the players be part of a new wave of explorers.
You'd have to tweak a few things, to be sure. Perhaps Vesk are showing up even though the Veskarium hasn't invaded. The Shirren may be unwitting harbingers of the Swarm. But it would create an atmosphere of exploration and "go forth" nature that would make a really interesting basis for a campaign.