A320 flight crew reported receiving a 'pull up' terrain warning while descending on arrival at night in a mountainous area. The flight crew executed an immediate climb and continued the arrival.

Narrative

We were inbound to fix ZZZZZ for an RNAV arrival to ZZZZ at night and with significant thunderstorm activity in the terminal area. ATC was clearly struggling and confused as they pulled us off the STAR and initially gave us direct to ZZZ VOR. They then gave us a heading; and contradictory and confusing holding instructions followed. At one point they simply said just stay north of ZZZ VOR--that was the extent of the holding instructions. Shortly after we were given direct to ZZZZZ and a descent to 14000; cross ZZZZZ at FL 200. We had to query ATC numerous times to confirm that they wanted us to do the ZZZZZ XX [arrival] for a Runway XXL landing vice ZZZZZ XY [arrival] for Runway YYR; which we had deduced on our own during a lack of information from ATC or ATIS. ZZZZZ XX for Runway XXL was finally confirmed. Inside ZZZZZ and at approximately 15000 altitude; ATC asked if we could proceed direct to fix ZZZZZ1. This is the standard merge point for the STAR and turns to this point are routine; however this was earlier than normal for the turn. We determined we could accept the clearance. Shortly after we were cleared to descend to 10000. On the STAR the altitude for ZZZZZ1 is 12000. At this point I made a horrible assumption-- having never landed from the east on Runway XX at ZZZZ; I assumed this was normal operations. I could clearly see the ground all the way down the valley to the airport at this point. I deselected weather radar on my ND (Navigation Display) and selected the Terrain display; oriented the chart terrain on the ND which appeared to be well to our left; and thus I continued the descent below 12000. The FO (First Officer) and I discussed the EGPWS terrain painting to our left; and that we appeared to be completely clear of terrain along our track to the runway. Shortly we started painting green EGPWS terrain in front of us; which very quickly started turning yellow. I was just verbalizing that I was no longer comfortable; but had not acted yet when we received a 'Caution; Terrain' EGPWS verbal warning. The FO recalls that it was not this EGPWS verbal caution but a 'Pull up Terrain' GPWS warning. I immediately disconnected the autopilot; selected TOGA thrust; and pitched toward full back stick. The EGPWS terrain that was displaying disappeared nearly immediately; the warning never repeated; and we were level at 12000 in about 20 seconds. I made a mistake here in that because we were visual and apparently cleared the threat so rapidly; I did not do the complete EGPWS Terrain procedure and never pitched to full back stick; which would have been appropriate since it was night time. The FO informed ATC that we had climbed to 12000; and they cleared us to maintain 12000 until ZZZZZ1 and cleared us for the ILS Z Runway XX. I reconnected the AP and autothrottles; re-armed the approach mode; and we conducted an ILS to Runway XXL followed by a sidestep landing on Runway XXR.Numerous lessons here for me. At the outset of the apparent struggles by ATC prior to our descent; we had correctly surmised that the airport had changed to Runway XX due to the thunderstorms interfering with Runway YYR. We thoroughly briefed the descent and approach to Runway XX in addition to Runway YY while we awaited a firm descent and runway assignment. I thought we had recovered well from all the confusion thrown at us early in the arrival; but I had clearly not and was still preoccupied with it. We briefed from the mountain flying guide that ATC may give you a clearance off the route and not ensure terrain clearance with the altitude assignment. This was in my mind as we descended below 12000 per instructions; but I did not verbalize it. I succumbed to my unfamiliarity with Runway XX; my disbelief that ATC could actually give us an unsafe altitude clearance; and it was all supported by what I initially was seeing visually outside the aircraft. In the back of my mind I knew staying at 12000 was what we should do; but I did not think clearly for those several minutes while collecting our thoughts and adjusting to a challenging evolution.