From the leaks we‘ve seen so far, and that teaser trailer Bethesda has shown back in 2018, I predict that the game’s backstory is about some kind of wormhole or portal that suddenly appeared in our solar system, which leads to a different solar system in a different part of the universe. And I think this different solar system will be where the game takes place.
I don‘t think we‘re going to be able to explore the whole galaxy or something, like in other space games, since the level of human technology we’ve seen in the leaks so far simply isn‘t advanced enough. I think the level of technology is similar to that of something like The Expanse, and humanity hasn‘t been able to leave the solar system yet – at least until relatively recently. The original teaser trailer clearly showed some kind of wormhole, or dimensional rift or whatever, and this is probably how humanity has been able to leave the solar system for the first time.
The game probably takes place several decades after the wormhole/portal was first discovered. Humanity has already built space stations, outposts, and even a few cities on the various planets, moons and asteroids of this new solar system, but large parts are still unexplored. If there are aliens, I predict they‘ll be more primitive, like in James Cameron‘s Avatar (or the game Outcast, for those who know it), and less like the aliens in Mass Effect. Though there probably will be some remnants of an advanced, but extinct, ancient alien civilization.