My name is ***** ***** I am an experienced criminal
In order to stop a car in the first place, police need only an articulable suspicion -- something less than probable cause
but more than a hunch. In this particular case, driving a car without its front plates would give the police a legitimate reason to stop the car.
From there, an officer can ask the passenger to show his or her ID, make him or her exit the vehicle and pat him/her down for his safety. This has all been true since the US Supreme Court
decided Terry v. Ohio in the late 60's.
If in the course of all of this the officer develops probable cause -- a reasonable belief that a crime may have been committed and that your son may have committed it -- he can do a limited search of the vehicle, seize what is in plain view, for example. To do a full search of the vehicle, however, he needs a warrant or an exception to the warrant requirement.
Was your son arrested or cited for a criminal offense? You have not said. In what US state did this occur? What is the question that you want to ask about this situation?
With further information I will finish my answer. I cannot tell if the impound was lawful without hearing more from you, but the stop itself looks proper.