Do you have to get car insurance right when you get your license even if you don't have a car of your own?

Generally, no. If you do not own a car, and you are not driving, you do not need insurance. Once you buy a car, or have a car available for you to use on a daily basis (or even weekly,) you will need to make sure you are listed on the policy covering that vehicle. For example, say Aunt Betty lets you take her car to school, but you do not own the car. Aunt Betty really needs to list you on her policy, but you do not need to get a separate policy for yourself. On the other hand, if Aunt Betty gives you the car and no longer insures it, you will need your own policy.