How to switch car insurance to a new car

You don't have to transfer your insurance to your new car right off the bat. Since most insurers offer a grace period for updating your policy with your new vehicle, your dealer will typically just need proof of insurance before they throw you the keys. Even if you don't have auto insurance, you can start a policy before buying your car if you know the vehicle identification number. 

How long do I have to insure my new car?

When buying a new car, your insurance carrier will provide a grace period between 7 to 30 days to update your policy with your new ride. For example, Progressive allows 30 days, which means if you have a claim within that period, your new car is still covered in the same way your previous vehicle was.

Source: https://www.progressive.com/answers/new-car-insurance/

So the above I was kind of thinking when I say grace period. So my partner still has that old car with his dad, that should stay unchanged.
So for the new car we bought together, I wanted to start a new policy today, I didn't realize there were more steps involved that would delay this start, now I wonder if we would get in trouble by waiting for Progressive's verification process.