No one, because there wasn't an Olympics in 1962. In those days, summer and winter Olympics were held in the same year instead of staggered; those years in this time period were 1960 and 1964.
The People's Republic of China's first gold medal in Olympic competition came at the 1984 Games in Los Angeles by Xu Haifeng in 50 meter pistol shooting.
At the Olympics, that was the 2004 Summer Games in Athens when he won silver in double trap shooting.
India won one gold medal at the 2008 Summer Games in Beijing, that by Abhinav Bindra in men's 10 meter air rifle shooting.
The country of Russia has won 7 Olympic gold medals in shooting, 2 in men's 50 meter free pistol and 1 each in men's 25 meter rapid fire pistol, men's 10 meter air rifle, men's 10 meter running target, women's 10 meter air pistol, and women's 50 meter three position small bore rifle. Shooters from Russia competed for the Soviet Union between 1952-1988 and for the Unified Team in 1992. The Soviet Union won 17 gold medals in shooting and the Unified Team won 5. Of the 17 Soviet Union gold medals 9 were won by Russian born shooters and of the 5 Unified Team gold medals 3 were won by Russian born shooters.
No country can "win" the Olympics.
Brazil first competed in the Olympics at the 1920 Games in Antwerp. The team won three medals that year, a gold by Guilherme Paraense in 25 meter rapid fire pistol shooting, a silver by Afranio da Costa in 50 meter pistol shooting and a bronze by the shooting team in 50 meter army pistol shooting.
Chen Ying (CHN)
Olena Kostevych (UKR)
Vijay Kumar won a Silver Medal for Men's 25 m rapid fire pistol
That was Edwin Vasquez in 50 meter pistol shooting. This is the only gold medal Peru has won in Olympic competition.
Olena Kostevych (UKR)
Andrija Zlatić (SRB)
Luca Tesconi (ITA)
Kim Jang-Mi (KOR)
Wang Zhiwei China (CHN)
Céline Goberville (FRA)
Jin Jong-oh (KOR)