Which means getting the experience somehow. Unpaid work is one (expensive) way of doing it, but so is getting into a related position and working your way across. QA is potentially a good path for this: hired to do simple things without the degree requirement, move into test automation, move across into development. Then you have it on your CV.
I agree that if you can hold out for a dev job, do that and save a year or two getting to the same place. If you really can't get a dev job and need the income, get a QA Automation job and start migrating early by asking to fix small bugs yourself, or work on the automation tooling.
At a smaller company, working on the build system and QA automation tooling might be more interesting and get more attention than what you would do as a jr software dev.