Cornelius Francis "Con" Dempsey got his start in the Pacific Coast League with Lefty O'Doul's San Francisco Seals. The side-arm hurler was born in San Francisco on September 16, 1923. His father, a building inspector in San Francisco, was born in Ireland.

Con attended Sequoia Union High School in Redwood City, where he won four letters in baseball, including a block letter. At the University of San Francisco, he played on the basketball varsity three years, and was selected as basketball All Star. He also lettered in baseball, and helped win the Northern California Baseball Association championship for USF.

He won his first professional game 14-0, and the opposition got only three infield hits, while he was striking out 11 and issuing only one pass. He came to the Oaks as a free agent in 1953, after injuring his arm. He says he owes the most in baseball to his parents for their continued encouragement, and to his high school coach.