I would suggest that you also open up a 529 account and start socking away some funds, even if it is just a small amount.
We too live in an expensive market in Southern California, as well, and socking away some money now will really help with incidentals.
My son almost received full funding at UCLA because of his major and his being an NMF winner where his Dad’s company would be sponsoring him.
You can always ask FA at each UC. There are private scholarships and foundation scholarships that require legwork on his part for most of the publics and privates in CA.