I have ASD and have been driving since I was 16 but it took me a good few years (at least) to really feel comfortable and not anxious while driving. I don't even really know how I passed my test (the second time...the first time...too anxious probably) but it was also a smaller city and more relaxed.
It wasn't really until I moved to a bigger city that I became more confident with driving (and even that took me awhile to be brave enough for the freeway) but eventually... it just comes.
So I will say, just give it time and keep doing it. It definitely gets easier. This is such bullshit advice I know, but it's all I've got.
I also will say, driving still kinda makes me paranoid but I use my hyper focus abilities to stay focused and then I usually end up driving well. Even if I'm in a bad mood or crying or whatever, I try to zone into just focusing on the road (this also helps my mood sometimes). And I'm quite jumpy when driving (horns, cars appearing too fast out of nowhere, etc). And I still hate driving with other people in the car still (I make them drive if they can)... this is absolutely social anxiety because of autism, haha.