Most states have something like this:
- at ~16, you become eligible for a driving permit which allows for supervised driving only
- getting the permit requires you to "pass" a pathetic 10ish question exam for which the literal questions and (multiple choice) answers are publicly available
- after 6-12 months (again, variable) you become eligible to get your full license
- to get a license, you usually need a guardian or affiliated adult to sign a form saying they taught you for over 40 hours of supervised driving.
- sometimes you also need a "safety class" or possible a "driver's education" class. Driver's education can be useful, since it's literally just a teacher riding around in a car driven by students and pointing out where the students go wrong. Safety classes are almost invariably useless, since they mostly just regurgitate rules of the road and obvious safety tips that most students immediately forget.
- Once you become eligible for a license, you go to a Department of Motor Vehicles (DMV), the same place where you got your permit. Schedule an appointment, and an employee will take you for a driving test. In the driving test, you have to show your mettle at serious challenges like parallel parking a car, stopping at stop signs, looking over your shoulder while changing lanes, and looking both ways before making a turn at a stop. This basic test has a less than 50% passing rate, but you can take it as many times as you like so even the worst drivers eventually jump through the hoop.
So basically the process you imagined but with more time and hoops where the government gets to charge you $$.