I guess that depends on which county you live in. Many counties are still in Phase 1a and don’t yet have an estimate of when they might get to the first tier of Phase 1b.
California has approximately 40 million residents. So far, the state has ordered 4.25 million doses, 4 million of which have shipped, and 1.6 million of those have been administered. Since each person requires two doses, even if all of those went to just LA County, I find it hard to believe they could have completed Phase 1a.
I think Newsom updated this last week, around the 13th, I believe. So, yeah, if your county has enough to move into 1b, they can do so. I’m in LA County, but I live in a city with its own health department and our city has moved into 1b because they have enough doses of vaccines.