B737 Undifferentiated or Other Model
Flight Crew Last 90 Days 218; Flight Crew Type 1500
Situational Awareness
Inflight Event / Encounter CFTT / CFIT; Inflight Event / Encounter Unstabilized Approach
Flight Crew Became Reoriented
Human Factors
Flying the Approach to Runway 3 at ABQ; approximately five miles from touchdown; the winds shifted and we were switched to a Visual Approach for Runway 26. Due to the last minute runway change; we were unstable at 1;000 feet and went around. Following the go-around we were set up for a right base to Runway 26 at 8;000 feet. There were strong winds at altitude that pushed us wider than I had realized. As we started to configure and begin our turn to final we began our descent. Passing through approximately 7;700 feet the Terrain Caution sounded. The Pilot Flying began a climb back to 8;000 feet and the caution silenced.  Due to the proximity of the runway and the pressure to land since we had already gone around once neither of us remembered at night a Caution Terrain required a go-around. After landing and discussing the alert we both realized we should have gone around and set the approach up again.  The last minute runway change forced us into being rushed and trying to just make it work. We should have taken an extra vector to slow things down so we could properly set up an RNAV backup.  Even though we did set the RNAV Visual on the first approach; the subsequent visual with Tower was very rushed and we failed to set up a backup approach to help us with terrain clearance.  Having an approach with altitudes would have prevented the early descent and the Terrain Caution.
After arriving at the gate; the First Officer (FO) and I reviewed the approach and realized I should have probably gone around for this warning since it was night. I did not intentionally disregard the alert; but my mental mindset was that I was not on 'Approach' yet due to being in the visual pattern and not on final and not configured to land. The time compression; I believe; also degraded my cognitive process. Next time I would go around and get vectored out for decompression and preparation time.First; with last minute changes ask for vectors out to relieve time compression. Also; use the RNAV Visual as a backup; as recommended. Add scenarios to training which include GPWS reactions other than pull-up. Of the many GPWS warnings we get that we can continue; maybe the few we go around for at night should be a go-around in the day as well so we don't have to qualify our response to something with critical timing.
On a night; visual base leg following a go-around due to an unstable initial approach; crew of B-737 experienced EGPWS Caution Terrain alert.