Usually it needs to be within 30-day since you lease

Check your insurance policy. Typically it requires you to notify the insurance company within 30-day window from the day you lease the car. The insurance coverage would start from day 1 when you get the car. Certainly the insurance premium increase will also start from day 1 you get the car.

On the other hand, why would you want to wait? Just give your insurance a call or do it online to add it into your insurance policy as soon as you get its VIN.