In 1939, he exhibited solo for the first time at the École des beaux-arts du Québec, then he collaborated with the Société d'art contemporain and the Musée du Québec. The government of Quebec grants him a scholarship to go and study in France. However, due to the recent war in Europe, Cosgrove found himself in Mexico in early 1940, where he remained for four years. He enrolled at the San Carlos Academy and took classes with Manuel Rodgriguez Lozano, then spent eight months as an apprentice to the renowned Mexican artist José Clemente Orozco. It was through him that Cosgrove acquired the fresco skills that were to have a lasting impact on his work: the application of thin layers of dry paint, the emphasis on form and composition, and the use subtle colors.