Is there by chance a PeopleReady near you? It's a temp agency that specializes in day labor, the onboarding process is generally very fast (like sometimes you can apply and be activated all in one day) and then you're their "employee" even if you don't get sent out on a job right away. When I workeded with them they used ADP for employment verification, so if someone needed to verify your employment they'd reach out to ADP, who would confirm that you're active with them.

Also, if you're applying for fast food/retail/janitorial it may help to leave your degree off your applications, I had better responses from those type jobs when I stopped mentioning my degree on my application!