First, it’s not clear to me why your insurance wouldn’t cover the damage for another 32 hours. It is likely that the new car takes effect on your policy in 32 hours. However, if it is replacing another car on your policy or being added to the policy as an additional car, your policy should have a provision that covers new cars temporarily until they can be officially added to the policy. Most policies will cover the new car for one week, as long as you plan to insure it on that policy permanently. If you fail to officially add the car, that temporary coverage becomes void.
You shouldn’t just worry about someone else hitting you without insurance. Everyone makes mistakes and you could cause an accident yourself. If that happens before your insurance is active, you will be personally responsible for the damage. It’s going to be tough keeping up those car payments if you have to pay for someone else’s car too.
It seems likely there is a policy that will cover this car temporarily. After all, you can’t get the car registered without insurance, so you must have shown proof of insurance at some point to be planning to drive the car now. That is unless the car is still registered to the dealership. In that case, you are covered under the dealer’s policy, as long as that registration is valid.
If this is your first car, and you have no existing car insurance, you should wait until your insurance is in place and registration valid before driving the car. Leave it where it is until the insurance kicks in.