My daughter did early entrance to first grade at a small private school. This is another way of saying that they tested her when she was 4 years and 9 or 10 months old (the age cutoff for entry to K at the time). She passed the end-of-K tests and a few end-of-1 tests, and they enrolled her as a first grader with subject acceleration at 5 years and 0 months when school started.

IMO, this is probably the best option in California these days. Small private schools tend to be more flexible in that regard. If you're going with public schools, I'd call and ask about their policies.