The tech industry is largely about experience. Sometimes you will work on fringe projects at work that aren't directly related to what you specialize in, but that's still experience. It's a seed. And then it snowballs.
Like if you're a language developer and they ask you to be a DBA in a pinch. You learn some SQL. It's bad, it's ugly, and all you had was Google. But now you "know" SQL. Now you're not just a junior programmer, you're a seasoned programmer with experience in multiple layers.
If work doesn't offer you this opportunity for fringe experience, there's always hobby/out-of-work/open-source stuff. You can make up for the lack of formal training and formal experience by giving yourself work. It won't be easy, but the option is always there.
If you're dedicated to your craft, have a genuine desire to do something, and have the brains to back it up, there's really nothing holding you back from jumping around to any arena of tech. Again, it won't be easy, but it's absolutely possible.
Edit: What I originally wrote is still great across the board, except for maybe the gaming industry. I hear they're insular and totally different from everyone else. So the barrier to break in might be much, much higher than say web development to database management. Still doable, but much harder.