ERJ-145 Captain accepted a non-precision approach to the mountainous terrain airport during night conditions. The crew became slightly high on the approach; increasing the descent rate to regain the vertical profile; which triggered the GPWS terrain warning. The crew regained the vertical profile and landed.

Narrative

Air Traffic control left us very high going into ZZZ. We were less than 60 miles from ZZZ when they initiated our descent from 22;000 ft. I asked the pilot monitoring to query ATC a few minutes earlier to get lower and we had difficulty getting through; so I switched to guard and they gave a frequency which was clearer. ILSXX but then as we got closer they asked us if we wanted the RNAV for straight in Runway XY. I discussed for a minute with the pilot monitoring and could not find any reference to ILS only at night in company pages; even though I could have sworn I thought I saw or heard something to that effect. Since we didn't see anything to that effect; we accepted the RNAV for straight in Runway XY due to its longer runway length. Pilot monitoring had terrain displayed on MFD as well. Runway was in sight pretty far out and I remained high on the VASI for most of the approach as a added safety margin due to the terrain and it being night. We still had altitude to lose as we got within 15 miles of ZZZ and the GPWS evidently interpreted our terrain closure rate as excessive; which is probably why we got the GPWS alert. We were on the glide path; stable and configured prior to 1000 ft. and 500 ft. and as far as I could tell; never in danger of ground contact.