not through Los Angeles

RosalieAnn answered pretty well but even with 126 you will be a bit in LA traffic. You have the Los Padres National Forest you will have to go completely north of and that will take you a long way up from Santa Barbara. And honestly some of the worst traffic I have been in is through Santa Barbara. What exactly are you trying to avoid?

It is going to be a longer and more circuitous route to avoid Los Angeles altogether, but you can do Phoenix to Palm Springs on I-10 and then cut up to Barstow.  Then take CA 58 to Bakersfield and then CA 99, and I-5 to north of Santa Clarita, and then CA126 and US 101 to Santa Barbara