Park was a cricket prodigy at Wesley College. His schoolmate Robert Menzies, future Prime Minister of Australia, recalled reading Shakespeare behind the school practice nets, "so that he could partake of the bard whilst watching Park bat." Park played for South Melbourne Cricket Club in the Victorian Cricket Association (VCA), and starred as a right-handed opening batsman, including a 315-run opening partnership with future Australian Test captain Bill Woodfull, for many years a club record. He became the youngest man to lead the batting averages for Melbourne Cricket Club. He was chosen as part of Warwick Armstrong's 1914/15 Australian team for a stillborn tour of South Africa: