I am buying a car in Arizona and driving it around the US. 15-20 years ago, I had a car (jeep) in the US for several years and was covered by Farmers.
Even if you don’t have a US driver license, you should still be able to find coverage with most insurance companies. You mentioned that you will be traveling around the US so it’s important to note that US insurance companies require a “permanent” address before they will issue a policy. The definition of permanent for insurance purposes would be the residence you plan on using for the next 6 months since that is the address the company will use to determine your rate.