Anton was born in 1868 in Lokve, Croatia. His parents were Stepan Plese and Maria Briski. He left Croatia in 1888, working as a merchant marine on a Turkish ship. He settled in Pueblo, Colorado in 1896. Through another Croatian immigrant, Josef Culig, he met Maria Cebulska, in Pueblo, and married her in 1898. Anton worked as a watchman in the steel mill, Colorado Fuel & Iron. In the early 1900s, Anton arranged for his sisters, Angelina (Lena), Milice and Danica to come to the United States and Pueblo.