I taught myself C++ when I was still in college for a digital media degree. As time went on, I was learning how to use various IDEs and build processes, and became active for a while on GameDev.net. I even made homebrew that natively runs on PSP hardware, using an unofficial community-built toolchain. But there was no Github to post my code to, and I didn't consider showing my game projects to the companies I interviewed at as a beginner, because I was not applying to game companies.
I eventually picked up web development jobs after graduation, but still doing some C++ hobby work up until around 2011. My most complex C++ project was a graphics framework built on the DirectX 9 API.
I would consider a C or C++ programming role for the right company, but you're correct in that it's hard to get your foot into with your kind of credentials. That is, unless you know someone who works at a company that is using it. A lot of it is gatekeeping, honestly, but there is a real need to understand how to write high-performance code with it.
Unfortunately most of my C++ dev work was lost in a hard drive crash. But I don't know if project age is a factor too. As in, would most companies even put stock in my ability to program in a language that I last used 7 years ago?