Legal Question in Criminal Law in California

First - it's not "probable cause" to pull you over - it's "reasonable suspicion". California law requires you to have two plates on your car (Vehicle Code 5200). If you don't have plates issued, you should have either a dealer's temporary permit affixed to your windshield or a temporary tag (the red 4x4 square with a white number to signify the month) visible on your windshield.

If they can't clearly see plates or one of those other exceptions, they potentially could do a traffic stop to see if your car was in fact registered.

You just described 'probable cause'. Besides, the officer doesn't need probable cause, only suspicion of something, or observing something wrong. Your remedy it at all, would be to bring an evidence suppression motion in court to prevent introduction of any evidence obtained in the stop.