There are other options.

Remember that schools can use state law to force your child to repeat kindergarten. However, they can't use it to force a child to repeat second grade. I'm not sure about first grade, because I can't find much information --- first-to-second may be a grey area, or it may be that everyone just moves to second grade. I don't know.

Once a child has been through second grade, they can only retain him because of poor academic achievement (as measured by grades and classroom achievement) or poor standardized test scores.

Schools have to create promotion and retention policies based on California education code. Search for "retain" in your browser to highlight.

Here's a sample of a school district policy that's been formatted for easy reading, unlike the CA education code.

See also here for an explanation of CA law.

My daughter skipped kindergarten at a very small private school in our area. We moved her to a bigger school for 3rd grade, and the principal had no choice but to promote her. His exact words were, "We're stuck with it."

I'd be wary about assuming that a child who had finished a private kindergarten would be moved quickly into first grade. Schools can be very skeptical about this kind of thing. For example, my eldest was offered a skip to fourth grade at a private school, but we had been thinking about moving him. The public schools in our area all said no to a skip, except for one, which said, "Well, we can put him in 3rd grade for at least 6 weeks and then decide." This was their way of saying no. Moving after 6 weeks would have been too disruptive for him as a new student, and they knew it.

Not all schools are so narrow-minded about acceleration, so my advice would be to call them and ask. Tell them something like, "Little Joey finished kindergarten at a private school, and he turns 6 in February. What's your policy about promotion to first grade?" If you don't like that answer, ask, "What if we kept him in private school for another year? What's about promotion to second grade?"

Some schools are wonderful and will try to work with you. Some have blanket NO ACCELERATION, EVER policies. Others are in between. My advice is to find out where your local principal fits on that spectrum and plan accordingly.