After purchasing a new car you need to have insurance on the car before driving it home so you'd need to get the insurance on the car before you drive off the lot.
But sometimes you can be temporarily insured by some dealers and have from 7 to 30 days to get insurance transferred from your old car to the new car.
As long as you inform your insurance company and transfer the auto insurance from your old car to the new car within 30 days then you should be fine but the grace period differs from state to state.
In one state it could be 7 days while in another state you have 30 days to transfer auto insurance.