I'll be the voice of optimism here...
I'll say that with the right connections, timing, and luck, it's conceivable to go from private to SWA in 3 years. Unlikely, but conceivable.
balls to the wall, you could get required ratings in under a year. From there, a place like Lakes hires low-timers. when I was there a few years ago, my sim partner had less than 300 hours. Granted he was in intern, but still, half my class had under 500 hours and weren't interns. maybe some current lakers can update me as to what kind of time they're hiring people with these days. anyway, it's possible to get hired there with very little time instructing. Yes, the pay & QOL sucks, but the good news is you would probably upgrade at 1500 hours, which at 100+ hours a month, is only a year away. Again, at 100+ hours/month, the magic 1000 PIC could only take a year. That would get you bare-bones minimums at SWA, which would be where your connections, timing, & luck would have to come in. Yes, I know that to be competitive at the moment, you need considerably more than that, but in 3 years, who knows.
Admittedly, my 3 year guess is on the extreme optimistic end of the spectrum. In all likelihood, it'll more than twice that long. I'm just offering another perspective.
I guess my advice would be the same as you'll hear a lot around here: go to a place where you can get turbine PIC quickly. airlines don't really care if it's turboprop or jet time. don't get sucked into the SJS.
good luck!