I got a job as an embedded C programmer after a MSc in "High Performance Computing". Weirdly the biggest supercomputers can use similar techniques to tiny microprocessors.
First of all I get why you like C, I loved learning it, and think it is a really elegant language (with obvious flaws).
I have some practical advice. Embedded is your best bet for getting to use C professionally. Are you into electronics at all? I would recommend getting some microprocessor/electronics kits, like the Arduino ones. If money is tight, Arduino clones are very cheap indeed. You could get going for < $20. You'll need a "bread board" some wires and a microcontroller. I remember getting a _very_ cheap oscilloscope kit too. You can make some cool stuff with sensors etc. I recommend any video by Ben Eater, if you want to know more about digital electronics. If you come up with a cool project idea you can write a blog post or even just talk about it in a cover letter. It would show you are very keen, even if you don't have professional experience.
You could also learn more about low level computing stuff by doing the excellent "nand-to-tetris" course, which shows you how to build a CPU. This is quite a commitment, and not essential, but I enjoyed it a lot!
Embedded Linux is also very widely used, so a project with a Raspberry Pi would look good too.
Good luck with a child on the way! Perhaps any electronics kits you buy could have a second life in 10-15 years...