My grandfather often talked about the US navy and army was so disorganized the days after Dec 7 th 1941 that if Japan wanted to they could have kept going all the way to the west coast.
Let's say Japan had this strategy:
how far could they have gotten before they were pushed back
What areas could they have established as strongholds
I just did about half an hour of fiddling with numbers. Keep in mind that this proposal is in the "no way" categorey.
Assuming an invasion of 10 divisions, you're looking at about 2.5 million tons of invasion shipping, plus another million tons in the supply chain. There's 4 million tons available, and the navy takes 1.8, so the requirement for California means no operations anywhere else, no supply of China.
Your oil cost for one year between supply and warships might be about 4.5 million tons (ie, 75% of the entire Japanese strategic reserve).
There would be no possiblity of resupply from the NEI, because there can be no offensive to the south.
I believe the USN's strategic oil reserves in California were about 40 million tons. I think California's indiginenous production was about 20 million tons per year. Since the entire Japanese reserve is exhausted for the offensive, you need to capture or produce 5 million tons per year in California, or you will run out of oil.
So, your plan of campaign would be to capture the USN's strategic reserves as intact as possible and then base your fleet in California. So, before invading California, it would be a good idea to see where those reserves and production were located and whether it was possible to capture them.