Prior military flight experience isn't required, but it can reduce the minimums from 1500 to 750 TT. From the USAJobs ad -

minimum of 1500 hours total flight time (100 hours of airplane and/or helicopter within the last 12 months) including 250 Pilot-in-Command and 75 instrument/night hours. Your full flight log book will be required at time of interview for verification.
NOTE: Up to 50% of the 1500 hour total flight requirement may be waived upon verification of prior specialized skills and experiences (e.g., general military flight experience and training, complex aircraft flight instructor experience, multi-engine aircraft time, night vision device operations, imminent danger, and terrain and/or over-water operations.)