The U.S. Olympic basketball team wore Converse All Stars in 1936.
Basketball made its Olympic debut at the 1936 Berlin Games, and the American team competed in Converse footwear. Converse All Stars were subsequently recognized as the official Olympic shoe from 1936 through 1968, linking the brand with the formative international history of the sport.
The 1936 tournament was unusual by modern standards. Games were played outdoors on tennis courts, and rain affected the competition, making the rubber-soled design especially relevant. The United States defeated Canada 19–8 in the final, a low-scoring result shaped partly by the wet conditions.
A frequent mix-up is 1948, when Olympic basketball was played indoors for the first time. That year was important in the tournament’s development, but it was not the first Olympic appearance of a U.S. basketball team in Converse All Stars. Another date sometimes associated with the shoes is 1968, the end of the period in which Converse was the Olympics’ official shoe. For the question’s first occurrence, 1936 is the canonical answer.