https://www.wikihow.com/Obtain-a-Cop...-in-California
I was born in California so I looked up the process because I remember it being much more involved the last time I got a certified copy of the birth certificate. According to this link, you fill out an application, find a notary public, send a check to the California health department, and wait fifteen days for processing. It's not the toughest process in the world, but it's the first step if you've lost your documents. I just got my social security card because I lost that a while ago and I used my birth certificate, but they did not give me a temporary. I waited about ten days for it to be mailed.
So assuming your driver's license requires these documents, you might be waiting about twenty five days before you can prove to your dmv both proof of identity and citizenship. Might there be ways to expedite this? Possibly, but you can imagine what it's like for someone who works six days a week to deal with government bureaucrats and to be sent home multiple times because the utility bill they're using for address in the state misspelled their name or something.
It is possible the process was easier back in the day, but it isn't quick I don't think.
