Applying for food benefits after losing my job

I lost my job as a software tester and my household is applying for SNAP for the first time. I am in Little Rock, in case local advice matters. I have a final pay stub, a termination letter and my unemployment approval. Is there an expedited option for people with very little income?

Thanks for writing this out. I went through something close to it last year, and it settled down once I kept a simple log of every call and form.