Platt was born in New York City, the son of Mary Elizabeth (Cheney) and John Henry Platt. Platt trained as a landscape painter, and as an etcher with Stephen Parrish in Gloucester, Massachusetts in 1880. He attended the National Academy of Design and the Art Students League in New York, and later, the Académie Julian in Paris, with Gustave Boulanger and Jules Joseph Lefebvre. At the Paris Salon of 1885, he exhibited his paintings and etchings and gained his first audience. In the decade 1880–1890, he made hundreds of etchings of architecture and landscapes. He received a bronze medal at the Paris Exposition Universelle of 1900.