Definitely give it some time. I didn't start feeling competent (and have a somewhat full linkedin inbox) until 5-6 years or so. Won't help with the visa situation though - I had a sweet opportunity to go work at a drone startup in Tokyo that I had to give up on because the Japanese government wouldn't let me. I could go for it (or something similar) now, but we'll see where my life is when I'm done at my current job.
I joined games (arguably harder in some ways to join than robotics), got real good at C++, then got word from a former manager about a self driving car company needing someone who knew games engines to do their 3D simulation.
Don’t worry :) I’m a game engine developer and they’ve been pinging me every so often for the past year or so. Speaking of which, what are your impressions of working there? (You may email me if you’re inclined or would rather.)