TLDR version: Drove a car at 15, learners licence at 18, crashed a car at 18, full licence at 21.
I learned to drive in New Zealand where the rules are no doubt different.
It took me a little while to get a full driver licence. Intellectually I knew how to drive a car and I think I'd had a go with someone's and by the age of 15 I was confident enough that I "stole" my Mother's Hillman Avenger one night while she was away. I took it out onto the highway then off on to some side roads and eventually on to some dirt roads that would've made for good rally driving. When I got home and went to apply the park brake I discovered that the poor performance from the car and that weird burning smell was because the park brake had been on the whole time. "I'd better do it again, properly." I thought to myself and headed out along the same route, this time with the brake off.
When I was 18 I don't think I'd done anymore driving but I'd started learning to fly and at about the same time I realised I might need to drive myself to the airport so I got a learners licence. I also stole my Mum's car again but this time I took a friend and while driving on the same dirt road I lost control and crashed it. Wrote it off. My clearest memory is of pointing at a rock face, travelling at reasonable speed, and my friend saying "shit shit shit shit shitshitshitshit!"

We were both ok. While walking home we saw a cat cross the road and decided we'd tell my Mum we'd swerved to avoid a cat and then lost control. Mum was disappointed that we'd crashed her car, though she was pleased we'd tried to save a helpless animal, even though swerving to avoid animals is a bad thing to do. She did tell me that she'd intended to give me that car shortly (d'oh!)
I realised how lame the swerved-to-avoid-a-cat story was when I told my flying instructor what had happened and he laughed and told me about the time he'd "swerved to avoid a dog". He knew it was bullshit as soon as he heard it. My mother believed we'd swerved to miss a cat until I finally told her the truth many years later.
So I just had a learners licence for a while, then the next stage is a provisional licence which allows you to drive where you like but with certain restrictions such as no passengers unless they are qualified drivers acting as an instructor and I think there may have been a curfew. I had to do a practical driving test to get the provisional licence and, as I had crashed my Mum's car, I ended up using my flying instructor's mother's car. I think it was a little Toyota Starlet or something. Anyway, he drove me to the testing centre and the first time I drove it was for the test. I did fine apart from climbing the curb while reversing around a corner. Three-point turns, hillstarts, etc were all fine.
To get a full licence after that was just a matter of spending a certain amount of time with a provisional licence
and putting an application in for a full licence. This I did not bother to do for quite some time.
Meanwhile I had continued with my flying training and finally, at the age of 21, I finished my commercial licence and within a couple of days got a job flying a biplane doing aerobatic joyrides. The job included driving the passengers to the airport and back to their hotel in a company van; a task I wasn't licensed to do. I was still on a provisional licence and that did not entitle me to carry passengers. My employers never asked if I had a full driver licence, they just assumed I had one, and I never told them otherwise. So for about eight months I illegally drove my passengers to the airport then quite legally took them flying in a high performance aerobatic biplane before illegally taking them back into town. I was very nearly caught out when I was pulled over for speeding in the company van with passengers on board. The cop asked for my licence and I told him I'd left it at home (which I had.) He sighed and told me to slow down

that was close.
I eventually got around to filling out the paperwork and getting a full driver licence. I was still 21 I think.
I'm much more responsible now days

.