No not at all.
I bought my first car at age 26 in Ohio. They wouldn't sell it to me without insurance, so I called up Progressive on the spot and set up insurance. It cost me about $100 to get everything set up that day, but then my monthly payments were like $48.
You can pay a full year or six months in advance, and it typically saves you money because insurance companies will charge your monthly rate + a few dollars for a processing fee each month. In my case, my current car insurance payment is $42 + $3 processing every month. So paying a full year upfront would be $42 × 12 = $504 instead of the $540 total I pay ($45 × 12) if I pay monthly. But that's just an option, not a necessity.