Countries don't compete in the Olympics, people do.
To "win" the Olympics, if it is such a thing, would be to be the country with the most and highest medals.
And to be the country with the most and highest medals, you need to be the country with the most winning athletes.
To get good athletes in as many sports as possible, a country need to make it easy for promising athletes to train, and to train well. Provide coaches, arenas, training camps, doctors, dieticians, sports equipment and so on.
win your country's Olympic Wrestling Trials.
Clara Hughes was the first person to win the olympic games
Vietnam
India
Canada
Brazil - Rio de Janiero
to win the Olympic gold to represent her country
A win by your own country (especially an underdog-type win) has in the past resulted in a patriotic pride, a renewed love for country.
The Olympic Games are not won by a country, individual athletes and teams win competitions.
The USA especcially with Michael Phelps.
There are no trophies in the Olympics just medals.
The last time I saw was China leading in Gold's.