Applying for food benefits after losing my job - any advice?

I lost my job as a customer-service rep and my household is applying for SNAP for the first time. I am in Chicago, 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?

I sent my last two pay stubs, the separation letter and a bank statement. I heard back in about 26 weeks, and my county offered an interview by phone.