Do you have a CS or EE degree? Are you based in the US? Are you willing to move within the US if so? Then you should be able to get an entry level embedded job with C, but yes you might have to learn or use some C++ as well. Embedded devices aren't as limited as they used to be so it's become common to have a full version of Linux hosting even real-time systems that were formerly bare metal or sitting on a minimal OS and written in C. With that change, C++ has started to enter the field more.

Look into the aerospace and defense industry in the US for a large contingent of C systems. Though greenfield ones may not be C anymore, there's a lot of C code out there needing maintenance too as they move to new hardware or add features.