Question

Do I have a legal three-day window to drive to NY in my new car without plates?

No, you don't have a legal "three-day window" to bring a new car to New York without license plates.

You need to obtain New York temporary tags from the dealership or DMV to legally drive the car until your permanent plates arrive, regardless of how far you need to go.

In all fifty states, including New York, you can only legally drive a new car with proper registration. You’ll need to put on temporary registration NY or temp tags for your car immediately. When you buy a new car from a dealership, they will usually provide temp tags so you can drive legally until you receive your permanent plates.