Your time in the 121 Regional world should be VERY QUICK by historical industry standards.

An unprecedented retirement wave is occurring across the entire industry and will peak around 2024, with an emphasis on the Big 3.

A reason you WON'T get a call from a Big 3 in the next 5 years will only be because you've got major skeletons. If you've got major skeletons just head to an AA Wholly Owned so that won't become the reason to hold you back from the eventual $300k+ paycheck.

If you've got a clean nose and a college degree, cast aside your obsession with a west coast base. Your job the next 5 years is to get a Job Offer from a Legacy. DO EVERYTHING and ANYTHING you possibly can do to expedite your interview date.

A wise newb pilot (who doesn't need to wait years for an AA WO FLOW cause of skeleton issues) will focus their efforts on getting hired at the regional which will offers:
1. Company Stability for the next 5 years
2. Time Building Opportunities
3. Upgrade Opportunities
4. Extra-Curricular Opportunities inside the airline. (Union Work, LCA, LVP, Sim-Instructor, Safety, Hiring Team, etc)

Check the boxes and move on to your career airline ASAP. Don't be the ignorant regional pilot who sits at home patting themself on the back because they got on with XYZ airline and they got the coveted home based option. Be the dude who got out there, got uncomfortable for a few years and did 100% of everything he could so when he does get to his Major Airline (ahead of all those ignorant "gotta be home based on the west coast or gtfo" pilots) he can then sit back and pat himself on the back, admiring his career seniority potential and watch the hundreds of thousands of dollars flow in to his coffers.