Air carrier flight crew reported GPWS warning on approach.

Narrative

On Day 0 we operated Flight X from ZZZ to ZZZ1; scheduled to depart at XA:59L. I was the Pilot Flying (PF) this leg. The winds were calm and the skies were clear at the destination so we planned to conduct a visual approach to Runway XX; backed up by the ILS. We programmed the FMS and briefed the approach. The Captain noted from the CCI page that terrain to the south of the approach could trigger a gear warning prior to the final approach fix on the ILS. We planned to approach normally with this in mind.After switching to the final Approach Controller; we were informed that the localizer for the ILS XX is out of service. At their suggestion we switched over to the RNAV XX. At this point we were already 25 miles away from the airport and had to work quickly. As the Captain programmed the FMS I continued the descent to 4;000 ft. for ZZZZZ. The conditions were VMC low-light night; but we had made visual contact with the airport. It was difficult to make out details of the terrain. As we approached ZZZZZ I noted that we weren't capturing the course because we were still in HDG mode from switching over to the RNAV approach. I switched to NAV; the FMS captured; and we turned to ZZZZZ1.I set the altitude for 3;000 ft. for waypoint; the final approach fix; and began a 500 ft./min. rate of descent. At this point I remember a few distractions that could've contributed to the issue. The Captain had noticed that the runway lighting was oddly bright despite his attempts to adjust it with the pilot controlled lighting; so I looked out to observe the adjustment. I also hadn't conducted an RNAV approach in a while and was attempting to think ahead to prepare for the final segment of the approach. We were also having to make CTAF calls and visually clear the local area ourselves because the tower was closed for the night. In an attempt to be proactive I set the altitude for the DDA of 1;400 ft.; not taking into account that the aircraft had not captured at the previously set altitude of 3;000 ft. for the final approach fix.The aircraft had continued to descend; as commanded; below 3;000 ft. as we reached the final approach fix. At this point we were approximately 500 ft. below where we should've been. The aircraft announced with the gear caution. The caution did not alarm us like it should have because we were expecting to hear the gear warning as we had briefed from the CCI page. Soon after; the terrain warning announced and it became clear that we were too low and the terrain in question was in front of us. I complied with the warning; pitched up; applied power; and almost immediately the warning cleared. At this time I was able to faintly make out the details of the terrain that was the cause for the alarm and could see that were now well clear. I rejoined the FMS generated glide path and course and continued the landing to ZZZ1 without further issue.In my opinion; this event was a result of expectation bias; a sudden change of plans; and an excess increase in workload at a critical phase of flight. Given the low light conditions and the vicinity of terrain to the approach; we should have treated the approach as if it were IMC. Our expectation of a visual approach lulled us into a false sense of comfort. The briefed expectation of the GPWS gear caution led us to downplay the threat that the terrain posed to the approach. These combined; along with the other distractions; led us into a false sense of security when we should have been at a higher state of alert.