You can do that without going to grad school. I didn’t land a design gig until about 2 years after graduation. In the meantime I worked at The Home Depot, as a mortgage temp agent, and a furniture repair tech. In my free time I took 2 classes at CCS and worked on my design projects and my portfolio.
Of course aim for a design job out of school, but don’t put off other methods of making an income, especially if you have zero work experience in general.