There are red license plates for this exact case. Car dealerships generally have them to allow for test drives and bureaucracy drives.

If you buy a car (which is currently unregistered) from a private person that doesn't have those, you just did something that the bureaucracy didn't foresee and at that point, the best course of action is to avoid as much of it as possible.

At this point I have no hope that any of this will getter unless the german state collapses completely.