Don’t you need to register the car in the DMV and get an insurance before you can drive away? That’s definitely the case in the parts of Europe I’m familiar with.
Car dealers over here are also "DMV deputies" for lack of a better translation. You bring your license, they type some things in their computer, print an ownership document and you get your car. The more permanent (creditcard sized) ownership card thingy will arrive in the mail a few days later.
Insurance is indeed mandatory, but you can get it online in 5 minutes. Or by phone. They call it "drive away coverage" that works immediately but requires signing the final policy etc within something like a week.
Getting insurance can be done online in about 5 minutes and the registration at the DMV equivalent is your problem (as the buyer) afterwards and can be done anytime in the next 2 weeks.
I can see that happening for second-hand cars but not for new cars that have to be issued new plates. But maybe things work differently in other countries. “Europe” is not really one place.
I got that kind of temporary plates once... at the DMV. It was quick, but they didn’t materialize magically when I needed them. Maybe it’s easier now, though.
Insurance is indeed mandatory, but you can get it online in 5 minutes. Or by phone. They call it "drive away coverage" that works immediately but requires signing the final policy etc within something like a week.