Pukstys parents came to the U.S. from Lithuania in 1949. He was born in Glen Ellyn, Illinois. He graduated from Amos Alonzo Stagg High School in Palos Hills, Illinois. His older brother Andrew was attending medical school in Lithuania, and returned home with a gift for Pukstys: a javelin. Thereafter, Pukstys quit the high school baseball team, and went out for the track team, throwing the javelin 155 feet in his first track meet.
For his first two years as an undergraduate, Pukstys enrolled in the College of DuPage in Glen Ellyn, and was a member of the DuPage Chaparrals track and field team. After his sophomore year, he accepted an athletic scholarship to transfer to the University of Florida in Gainesville, Florida, where he was a member of the Florida Gators track and field team. He graduated from the University of Florida with a bachelor's degree in public relations in 1992.
Pukstys broke his first American record in June 1993. His personal best was a throw of 87.12 meters in 1997.
The 1920, 1928, 1932, 1992, 1996, 2000, 2004, 2008 and 2012 championships incorporated the Olympic Trials, otherwise held as a discrete event.
Ken Churchill had the longest throw in the 1932 competition (which doubled as the Olympic Trials), ahead of Malcolm Metcalf. However, Churchill qualified for the final only due to a late rule change by the U.S. Olympic Committee, allowing eight rather than five finalists. As this rule change applied only to the Olympic Trials, Churchill is considered to have won at the Trials and Metcalf at the national championships, even though they were the same meet.