Applying for food benefits after losing my job (update)

I lost my job as an IT help-desk technician and my household is applying for SNAP for the first time. I have read a lot of threads here and could not find my exact situation. I have a final pay stub, a termination letter and my unemployment approval. Is there an expedited option for people with very little income?

Some local food pantries can help while the case is pending. Try calling 211 for one near you.