Vintage Vehicle Registration in California

I'd get the car titled with no plates or registration to show ownership.

Do this before doing any work to the vehicle. If you try to title it after the restoration with a $200 bill of sale as an example, they will nail you to the wall...

No need for anything but a bill of sale in CA. Title is handy but not necessary. They will do a vin verification which on something that old may require a trip to CHP office.

Once the restoration is complete, you can walk in and get plates/registration usually without them ever having to look at the car.

Good luck