About 95% of my traffic so far has come from my own followers in social media.
This was largely true for me too, for the first half-year or so — maybe 90% was readership I brought from elsewhere. I started with Twitter and got modest engagement, then found that Facebook was a more effective place, for me. To a lesser extent Quora helped. I’ve not tried other platforms myself, but non-trivial traffic also came from people reposting on Reddit and Instagram.
I gradually built my following there and on Medium by 1. publishing frequently and regularly, and 2. by being very responsive to readers, spending as much time in correspondence as I have in my writing proper.
After five months or so I hit some kind of ‘critical mass’, and things took off (relatively speaking; I am not in the ‘big leagues’). Suddenly 90% was coming from Medium and readership jumped two orders of magnitude in two months.
What happened? Probably getting on the Editor’s Picks list (which gets you onto the front page), plus a couple recos from @ MediumStaff.
And how did that happen? Not certain, but probably from 1. gradually moving up the ranks in my primary categories/tags (LGBTQ, ThisHappenedToMe), and 2. getting stuff into a few decent-sized Medium Publications (5–25K followers).
Also, I hate to admit it, but I started using more provocative titles. That probably helps get people to have a look, but a high ‘read ratio’ comes from engaging writing, of course.