Are you submitting under a NWP or do you need a project specific permit.
If you qualify for a NWP (my guess is you're submitting under NWP12), read it carefully - you may or may not need a PCN.
If you need a PCN, I'd assume 60ish days after you first submit (mileage will vary heavily depending on the regional office)
If you need a site specific permit, be prepared for a long process, as it can include public meetings so any "public comments can be heard". Unfortunately, I'd budget for a minimum of 6 months - but be prepared for 9-12 months.