Booster... Green(?) Elseworlds pitch
Ok so I know very little about Booster Gold other than the base concept of "former sportsball star from the future steals tech from a museum and goes back in time to pretend to be a hero for fame and fortune (but eventually becomes a real hero)" so forgive me if this is OOC but consider this story idea:
When Booster travels back in time, he does so a little carelessly. So instead of arriving wherever it he does in canon, he instead lands in a certain alleyway next to a club in Los Angeles. And when he steps out of the Time Sphere, he comes face to face with a very surprised Guardian of the Universe.
Ganthet, who is still half-mad with grief from witnessing everything he and his brethren had worked for being brought crashing down by their Corp's greatest champion, decides that one human is as good as the next. So he hands the last Green Lantern ring to Michael Carter and fucks off to who knows where.
Poor Booster is in shock, because this all sounds very much like one of the exhibits in the museum he used to work at. Then he checks the underside of his Time Sphere and starts to panic. Because crushed beneath the time machine is the dead body of one Kyle Rayner. The man who kept the light of the Green Lanterns alive long enough to reignite the Corps that still protects the universe even in the future that Booster comes from. Or at least he would have, if he hadn't been turned into a smear on the pavement before he could achieve any of that.
And just like that, Booster's original plan goes up in flames. It's one thing to become a minor superhero for profit, that shit probably won't cause too many problems for the space-time continuum. But accidentally killing the Green Lanterns' Torchbearer? That's the kind of change that prevents your own birth because your grandma got blown up in an alien invasion or something.
Obviously, Michael has to fix this somehow, before reality itself falls apart. He wracks his brain, trying to come up with a possible solution. Then it hits him.
He can't bring Kyle Rayner back to life. So he'll just have to be the last Green Lantern himself!
Which then leads to Booster speedrunning the aftermath of Emerald Twilight, redeeming Parallax and helping found the JLA with nothing more than vague recollections of stuff he read in history books and museum exhibits. It keeps the timeline intact at least, but is also horribly, horribly stressful for poor Booster. It's like having to pass a history test that he barely studied for, but the stakes for failing is reality itself unraveling!
The worst part of it is, all the other heroes he works with and people he saves are genuinely grateful and praise him as a true Green Lantern, which only makes Booster feel like even more of a fraud. He's just playing a part that he has foreknowledge of, a role that wasn't even supposed to be his!
(And because he's the only one- besides Skeets- who knows this, there's no one to tell Booster that he might not have started out as worthy of the ring, but he's grown into it the same way that the original Torchbearer was supposed to)