In teacher centered classrooms, students cannot develop autonomy in their learning. They are usually totally dependent on their teachers. Especially, in test oriented countries, developing autonomy in learning is a great problem.
I am not sure that any learning is reasonably called "autonomous", but if I may replace this term by "self-regulated", I can say that self-regulated learning begins as soon as primary eduaction. Review studies show that teachers in primary education in Germany use several avenues to reach that goal (cf. Dignath, C., Büttner, G. & Langfeldt, H.-P. (2008). How can primary school students acquire self-regulated learning most efficiently? A meta-analysis on interventions that aim at fostering self-regulation. Educational Research Review, 3, 101-129.)
I am not sure that any learning is reasonably called "autonomous", but if I may replace this term by "self-regulated", I can say that self-regulated learning begins as soon as primary eduaction. Review studies show that teachers in primary education in Germany use several avenues to reach that goal (cf. Dignath, C., Büttner, G. & Langfeldt, H.-P. (2008). How can primary school students acquire self-regulated learning most efficiently? A meta-analysis on interventions that aim at fostering self-regulation. Educational Research Review, 3, 101-129.)
In my country INDIA, quality education is still university-based and premier institutes offer higher education in their campus-based architecture.
However, open education is an alternative paradigm of education which is also quite profuse in India.
India has the largest open university of the world with more than 3 million students, the Indira Gandhi National Open University (IGNOU).
Distance Educational Council administers such open universities in India.
As you have asked about autonomy, students seeking Higher Education (Tertiary Level) mostly get the benefits of this open education.
But still there is a gap of academic status between the formal university-based education and the other forms of open and online education in India, the former being leading in superiority.