Moore's career as a mountaineer started early, with an ascent of Chimborazo and the first ascent of Sangay, both in the Andes of Ecuador, in 1927. In the early 1930s, he made the first ascents of Mount Bona and Mount Fairweather, both major Alaskan peaks, with Allen Carpé, and he also made the first unguided ascent of Mount Robson in the Canadian Rockies.