Yup, you can call them to get the Case # over the phone.

I called NVC today to inquire about my application. They said they received my application from USCIS on 05/08/2018, but have not generated a case number. Maybe in another 2-3 weeks.

Their phone number is: (603) 334-0700
Monday through Friday from 7:00 a.m. to 12:00 midnight EST, excluding holidays.

https://travel.state.gov/content/tra...formation.html