I didn't even have a CS degree, but a M.S. degree in Physics/Astronomy; in fact, I never took any CS classes, but did quite a bit of programming related to my college classes after doing some Fortran programming in a job during high school. I started in a small company doing some CAD work, and demonstrated my programming skills through automating some of my tasks and helping automate some large tasks. This led me to programming the company's main applications. This is how I started. My suggestion is to be hired by a small company where multiple skills are much appreciated. It's always risky to work for small companies, but it is a good way to move through multiple disciplines getting work experience.