Where at in LA and how far are you willing to commute? AMR Ventura Co AND San Bernardino Co you'll be the EMT on a Medic/Basic rig that does the actual ALS transports.
The only thing I know about Southern California Ambulance is that they are an exclusive IFT only company, basically meaning lots of hospital discharges, picking up nursing home patients for pre-scheduled medical appointments, maybe the odd nursing home to ER for "abnormal labs", and lots of nice reliably profitable dialysis runs. There's definitely tons to learn doing that work and there is always the chance that one of your patients may suddenly get really sick on you, or someone will attempt to push a patient on you that really should not be a BLS IFT, so yeah you need to stay on top of your assessments....but it'll get reeaaallll easy to become complacent when 99.99% of your calls the only skill you do is basic vital signs because the patient doesn't need more than that. So just know and expect going in that that's what that job is and you won't be doing any "cool EMT stuff" you learned in class like bandaging and splinting and all that.
(Granted the reality of 911 is that the majority of calls aren't very different...but as someone who works for a 911 provider and little desire to go IFT I certainly understand the appeal of it haha) The 4 private ambulance 911 providers (AMR, Care, McCormick, and Schaefer) ALL hire EMTs with no experience. Now if you just fired off an online application and didn't hear back, that may just be because they half expect you to put on your suite and tie and show up to hand deliver your app (don't just leave it with the secretary at the front desk, ask to speak with the hiring manager, find a crew from the company and simply ask them who that is if need be). If you can get hired by So Cal Ambulance you can be hired by McCormick or Care or AMR....