Can anyone point me towards a source to find out which majors or regionals have a base at or near LAX that is junior?

Currently Compass is the only one that comes to mind. Most new hires are getting LAX right outta training. Skywest has an LAX base as well but you're going to have wait. Don't know the exact time frame. Buddies of mine that fly there say expect about 4 months to get LAX as a FO. Time frames vary though. Most mainline carriers (AA, UA Delta) have LAX domiciles.

Majors right now seem pretty junior for new-hires at LAX, probably due to high cost of living. But that's just to get into the base, more senior folks tend to stick around (they can afford it) so it will likely take longer for your seniority to progress long-term at LAX.

I’d be interested to know as well.

Thank you!