Boarding was tight in my suburb even 40 years ago. I found an empty stall in a self-board backyard, and then had a month to buy a horse. It all worked out well!
These days in a tight market for a returning or beginning rider, I’d suggest taking lessons or leasing at a barn or barns, and then working towards full ownership with the guidance of the trainer or barn manager.
If you were coming in with a horse from another area, you’d probably want to contact all the likely barns well in advance of the move, just like you’d do for finding an apartment rental, and asking to be put on their waiting list.
In any case, even in a tight market there will be turnover, and there will be a little slack at the outer edges of a market, for instance when you get a little too far to be a reasonable drive for most people, but you can put a horse there on pasture for a month or two while you shop for a more reasonable location with full board and an arena.