I ran into something similar as a Dutch person trying to buy a car from Germany. The initial plan was to drive the car back from Germany, but to do this I had to get an export license plate. This can only be done in the municipality where the car was sold, and they told me I was lucky because I could get an appointment quite quick, which was a month and a half from now. I would also have to bring the car to the Straßenverkehrsamt. How I would have gotten the car there was also a mystery to me, as I did not have a license plate and to get a license plate I would have to bring the car there. If I did somehow manage to do that though, I would have to get a physical license plate made and then get temporary insurance. Not a single German insurance company said they could insure the temporary license plate, as I was not already an existing customers of theirs. I ended up just renting a car transporter and bringing it home that way.

The process of getting a license plate once home was actually a breeze. I used the website of the Dutch Vehicle Authority to make an appointment (for the following day at 2pm) and they gave me a temporary license plate. I simply had to write this on a piece of cardboard and put it where the license plate would go. Called the cheapest insurance company to get temporary insurance, which was no problem, and simply drove the car to get it inspected.