A319 Captain reported during the descent receiving a GPWS alert with the aircraft flying towards terrain resulting in the flight crew climbing to a safe altitude and ATC cleared them for the approach where they landed safely.

Narrative

ZZZ to ZZZZ. ZZZZZ to ZZZZZ1; cleared (PPOS) present position direct ZZZZZ1 and descend to FL240. Approaching ZZZZZ1 we were then cleared ZZZZZ1 [arrival]; descend to 14000. After passing ZZZZZ1 we checked in with approach and were further cleared direct to ZZZZZ2 and descend to 14000. ZZZZZ2 is the transition point from the Arrival to the RNAV approach. As we were passing over ZZZZZ3 approach gave is PPOS direct to ZZZZZ3 and descend to 10;500. As PM (pilot monitoring) I checked the terrain on this direct route the arrival and approach chart and determined the highest point was 8000. We leveled at 10;500. At this point; the weather was partly cloudy; haze with 6 miles visibility and we could clearly see the ground in front of us. About 14 miles from ZZZZZ3 PM requested lower. We were given a decent to 9000' and approach asked if we had the terrain in sight. PM responded with affirmative and figured we would have 1000 feet on this track towards ZZZZZ3. PF (pilot flying) started a slow decent. We could visually see the hills and we were nearly on top of the ridge line descending thru about 9;300 feet. (Estimate we were about 5 miles from ZZZZZ3) We got a GPWS 'Caution Terrain (amber)'; 'Terrain; Terrain; Pull Up' (red) - all run together. At 'Caution Terrain' the PF almost immediately clicked off the autopilot; arrested the decent then started a slow climb back up to 9400 feet. Then the GPWS showed us clear and green again before we could verbalize anything including 'My Aircraft; TOGA'. This all occurred in what seemed about maybe 12-15 seconds (difficult to tell but it seemed like a very quick event). At this point; it was visually obvious we were past the last hills and we reestablished the automation. Approach then cleared us for the visual and contact tower. We then set 8600 feet for ZZZZZ3 and used the RNAV for guidance to the visual approach. The rest of the flight was uneventful. The crew debriefed after shutdown at the gate. Both of us felt we had good situational awareness; briefed the terrain threats and used all the tools available to ensure terrain clearance on the route we took. We had good visual with the ground and set appropriate altitudes to where we were. The GPWS was a surprise because it went thru the caution to terrain alert so quickly then back to green with no further alert.CauseHindsight; we should have stayed on the RNAV arrival to ZZZZZ2 and not cut the corner even if it looks safe to do so. There was no other traffic or time constraint. Especially in this country; I need stick to the published arrival and approach. Because it was Day VMC; that was the one factor that made the vector seem like an acceptable clearance. Because we had the terrain insight; we felt that we were aware of where we were & operating at a safe altitude. At night or IFR I wouldn't have never considered it. I don't plan to make that mistake again. We ran the software long flight review but it started after our event.