Same here, though I was aided by being able to be really confident about stuff when people came calling with the checkbook and a quick study once I'd landed a gig. I learned to do what we would now call "sysadmin stuff" (manual administration of hardware) as a kid because I broke my Linux machines a lot. Then I went into the web development gristmill for a while. Ended up leading a multi-platform mobile team with zero mobile experience because "you're a good developer, you'll pick it up" (I did); I literally went into a devops role knowing no Ruby (to say nothing of Chef) under pretty much the same rationale.
"Fake it till you make it" is real, but then you gotta make it. ;)
Therein lies the best career advice I could possibly dispense: just DO things. Chase after the things that interest you and make you happy. Stop acting like you have a set path, because you don't. No one does. You shouldn't be trying to check off the boxes of life; they aren't real and they were created by other people, not you. There is no explicit path I'm following, and I'm not walking in anyone else's footsteps. I'm making it up as I go. - Charlie Hoehn
I've worked with developers who fully understand the systems they are deploying on, and developers who develop for an abstraction of services rather than a real world environment - I tend to prefer the former to the later because the deployment process is much less taxing, even though the later tend to have better luck moving their software to another platform in the future.
But I'll echo you, every time I've learned something hard, it's because I got way out of my depth and had to learn how to swim all over again.
How you get there is up to you. My own path was freakishly meandering. Don't be afraid to get out of your depth, but try to have a mentor around to stop you drowning.
And remember that DevOps is a mindset, not a job. If someone tries to setup a "devops team", run away.