In 1896, when the first modern Olympic was held, The first medals of the modern Olympics awarded in Track and Field, more specifically, the Triple Jump.
Jack Beatson
Men's football was a demonstration sport at the 1896 Games in Athens and became a medal sport at the 1900 Games in Paris. Great Britain won the first gold medal. Women's football became a medal sport at the 1996 Games in Atlanta. The United States won the first gold medal in women's football.
Badminton is the official sport of Indonesia. Indonesia has won a Gold medal since the sport was first introduced in the Olympic Games.
Tug-of-War in 1900
Andy Murray won the gold medal for men at the 2012 London olympics. Although he is from Scotland his medal counted toward the Great Britain total-- a first gold medal in this sport!
Basketball
Hawk was 27, when he won his first gold medal. -Swan
Vũ Thị Hương won Vietnam's first Olympic gold medal in the sport of shooting at the 2016 Summer Olympics held in Rio de Janeiro, Brazil.
Nigeria won her first Olympic gold medal in 1876
Field & Track
No, and Canadian football is not an Olympic Sport.
Rugby is not an Olympic sport. The last Olympics where rugby was a medal sport was the 1924 Games in Paris.