Air carrier First Officer reported receiving a GPWS terrain alert on approach to MMMM/MLM airport.

Narrative

I was flying into Morelia. The pilot monitoring and pilot flying did brief the plate and company notes before flying this approach. Flying VOR Y RWY 23 approach. I believe before DME 12.0 I realized quickly that I was too high; I believe we were at 10;000 FT MSL. I told the pilot monitoring that I was too high. At that point I do not recall exactly what we decided to do. I believe we chose to utilize flaps 9; speed brakes out; power idle; and more of a descent rate. Within seconds of trying to drop quickly; I realized again that we were just too high for this approach. At that point a 360 turn was suggested. The pilot monitoring then asked ATC if we were allowed to do a 360. Which ATC said; 'it was more than fine'. During the 360 turn and descending we received one audible warning of 'TERRAIN'. At that moment I pilot flying leveled out; stopped the descent; full throttle and started to climb. The audible warning was [heard] once and went away. The pilot monitoring advised to keep the turn coming. As we finished the turn; we were back at our original dilemma of being too high. We tried to drop quickly again with no success. At that point; we chose to conduct the go-round procedures with no further issues.I believe why we were too high is we were trying to make the box more suitable for our approach.I read this plate over and over after this incident. I know we might think certain things are easier to do; but I will just fly the missed approach. That is what it is there for.