FYI as of 2023, I took delivery of my new car on March 31 and it's now May 31 and hadn't received my plates. I did an online chat with the CA DMV and they said that my permanent registration just went through on May 25 and I should receive the plates by June 25. So, apparently 2-3 months is what it is taking now to get your CA new car plates in 2023.