I suggest calling the state office of the CA DMV. I've been told that the state info phone line has more knowledgeable people than the local offices. They can tell you the process that is acceptable to the DMV.
If there is a VIN on the car, the CHP can inspect that car and if it is not in the CA DMV system, they can verify the VIN belongs to the car and can issue a form that the DMV will accept for registration (along with a written statement that the car was bought at a wrecking yard out of state and brought to CA).
If the car does not have a VIN, the CHP can assign one to it and will rivet the new number onto the car and then you go to the DMV for registration. This is the process that I had to go through with my '28 truck, which had been off the road for many decades and had no car ID plate. I also had to provide a statement of fact saying the car was on private property for all those years.
Cheers, Dean