Applying for food benefits after losing my job - what worked for you?

I lost my job as a software tester and my household is applying for SNAP for the first time. Any experience at all would help. There are 16 people in my household. 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 14 weeks, and my county offered an interview by phone.