A lot of places “extend” their permanent team through long term or regular contractors. I have several friends who have been operating as contractors in various cities to a multitude of design firms for over a decade. Some people prefer to work that way, and some place prefer to hire contractors.
I graduated in a similar situation (albeit 15 years ago). I didn’t have a lot of experience, and it was tough to get the first gig. I contracted at various places, which built my network, my portfolio, and my confidence, until I found that golden first job.
The most important thing is to keep moving. Keep reach out, keep building your portfolio. Do whatever it takes to keep yourself fresh in the eyes of others and for your own personal motivation.