Rey grew up in foster care, but her mom's parental rights were never officially terminated, so she's still hoping Mom will show up someday. She's worked at Unkar Plutt's junkyard out near Joshua Tree for years, and once she aged out of the system and needed a place to stay, he let her set up housekeeping in a rusted out container in the back of the yard.
Finn is from LA, and everyone he knew was part of the First Order gang, and so he was too. But one day they give him a gun and tell him to take out some rival gang members as an initiation, so he runs to the only place he can think of: the (undetermined branch of the military) recruiting station down the street, where he tells the recruiter he needs out, immediately, like, today.
Still on the fence about whether Poe is the recruiter or not, but more likely he's someone Finn meets in flight school. Probably a trainer. And it's seriously frowned upon to have relationships with subordinates so Poe does not hit on Finn, because he is not Creepy Dude, okay, he is better than that, and Finn is just making those eyes at him because Poe taught Finn to fly, and flying is the best thing ever, get ahold of yourself Dameron.
Finn has a terrible junkheap of a car, but he likes going out to interesting places on days off, and so he shows up at Rey's junkyard one day with steam coming out from the hood and totally dejected because there's no way he'll be able to pay for repairs and he'll have to take the bus back and no more adventures for him...
And then Rey shows up and she's gorgeous and also fixes his car and doesn't charge him for the labor, he's pretty sure she even undercharges for the parts, and she offers to show him the places in the park that nobody goes, and well, Finn is in puppy-eyed love with her pretty much from that point.
Romantic endgame unclear, friendship-ot3 for sure, lots of wind and sand and desert heat and the sheer goddamn weirdness of the California high desert, exploring the moral complexity of military-as-escape, would end up being way longer than I can write, but the idea interests me.