Air carrier Captain reported a GPWS terrain warning due to a late turn to the final approach course and an overshoot of the final approach. The pilot climbed and re-intercepted the final approach and landed safely.

Narrative

Cleared for visual rw 24. We were on downwind and descending from 6k on north west side of field. I said; I've got the field in sight; and will back ourselves up with the RNAV Y 24 and to be aware of mountains. I didn't give ourselves enough room to make the 180 to final and overshot the final approach course. I was navigating back to WUDAG which is final approach fix; and had our altitude set up at 3200 ft which is the FAF altitude (3220'). However; bc of my initial overshoot of final and desire to intercept the approach at the FAF; our direction of flight was into rising terrain and I set off the GPWS. I immediately disconnected the autopilot; climbed up and turned left to intercept the final approach course and landed uneventfully. Lesson learned would have been to give more room on base for turn to final or just accept the overshoot and fly a visual approach where I was offset away from the terrain.Cause: Too tight of base turn to final which caused an overshoot which pointed us back at terrain as we looked to rejoin the final approach course.Suggestions: Either get vectors for the RNAV or just give myself more room for the base leg to prevent an overshoot which caused us to be pointed at terrain in front of us. As soon as I realized that terrain would cause a GPWS alert; I should've stopped trying to join the RNAV and just flown a visual approach.