Running a bake sale for a charitable cause falls under different rules, but in this case it sounds like the funds would be for your family’s use (not donated to a nonprofit).
So in that case, if we want to get really technical, the answer is yes, in CA you’d need a permit to legally sell baked goods, and zoning laws might prevent you from selling out of your front yard.
In more practical terms, what you are trying to do is extremely common, and almost nobody is going to stop you or complain. In fact, if anything, they will support you! This is especially true if your kids are helping run the operation. I’d personally say go ahead and don’t worry about the legalities.
Now, if this turns into a weekly thing, and/or you start to sell elsewhere, that’s where I might suggest looking into getting your cottage food permit.