The fist time a car drove itself in a track with no human intervention was the 1980's. That is when we had self driving cars. Its been here for a while, its not coming.
The technology has been slowly improving since the 80's, and especially since machine learning came along.
Self driving, like all technology, wont just appear and suddenly no one everywhere will have to call a uber after a good night out anymore. It will phase in with the crappy versions first, that do lane keeping, emergency breaking ext. And over time get better at those things, and keep including new things it can do.
By the time YOU experience self-driving cars, early adopters will already be looking for the new thing.
If you have a Tesla with Autopilot, your getting the first glimps now.
In 20 years there will be some angry wife that wants drive her Tesla through a security control gate, onto a harbor jetty and park it on her soon to be ex-husbands new yacht. But because the Tesla wont allow her to do all that people will say the software is not there yet.
Self driving will happen in incremental steps.
One day it will just be part of everyone's lives and most will not know how it happened.
If your asking for full-self-driving with no intervention by people in any circumstance ever conceived.
That will come soon after AI gains the "singularity", i.e. super intelligent general intelligence. This may be never to 10's of years away.