Božić's first notable Himalayan climb was the 1979 ascent to Mount Everest as a member of the Yugoslav expedition that used a previously unclimbed West Ridge route, known today as the Complete West Ridge. A similar path was chosen by a 1974 French expedition that ended in disaster when six climbers were killed in an avalanche, but Yugoslav team leader Tone Škarja modified the route so as to avoid the avalanche fall-lines. The large expedition, numbering 25 climbers, arrived at Base Camp on 31 March and progressed smoothly through four additional bases. Andrej Štremfelj and Nejc Zaplotnik reached the summit on 13 May, followed two days later by Stane Belak, Ang Phu and Božić (becoming the 85th through 89th persons to have climbed Mount Everest). On descent, the weather worsened quickly and the team were unable to return to Base Four before dark and were forced to spend the night in a temperature, without tents or sleeping bags, at an altitude of . According to Božić, at the time this was the highest ever overnight bivouac in the open, and the closest he had ever been to death. They managed to survive the night, but on the following day, Ang Phu slipped and fell to his death going through the Hornbein Couloir.