Count Dressler was a Human criminal who was manufacturing hydrogen bombs at a time when Earth was negotiating to ban them. He was forced to escape from Earth when his small nation was surrounded by thousands of troops. His rocket ship left for a planet hostile to Earth, and the natives there taught him the secrets of voodoo. He then proceeded to create a life size papier-mâché representation of the entire Earth, which he could then use to attack the real thing. (TOS comic: "The Voodoo Planet")

The time period in which his backstory occurred is not clear. It appears to take place during a time of upheaval, perhaps after World War III, but Captain Kirk references the events as if they're in the recent past, and Dressler himself has not aged significantly.