Which small-town soccer team from Ontario won a medal at the Olympics?

The Galt Football Club (Galt was a town that has since become a part of Cambridge, Ontario) didn't just win 'a medal'; they won gold at the 1904 St Louis Olympiad. Further football gold eluded Canada until their women's team won in 2020.

https://www.olympics.com/en/olympic-games/st-louis-1904/results/football/football-men
https://www.thecanadianencyclopedia.ca/en/article/1904-galt-football-club

Galt FC won the football gold medal at the 1904 Olympics in St Louis. There were only three entries, Galt FC and two from the USA, Christian Bothers College & St Rose Parish (due to the costs of travelling to the USA). Galt FC won both its games in the round robin tournament, 7-0 vs. CBC and 4-0 vs. SRP, to win the gold medal. Galt is now part of the City of Cambridge, Ontario.

It would have surprised no serious follower in the city of Galt that the Galt Football Club won the right to represent Canada in 1904 at the Olympic Games in St. Louis. The club, comprised entirely of local talent, had a 25-year record of success in the sport we now call soccer. With 44 championships during that time, Galt was considered the football capital of Canada. A 2-0 victory over their main rivals, the University of Toronto Varsity Blues, guaranteed a trip to St. Louis ... [in St Louis the] weaker of Galt's opponents were defeated 7-0 in the first contest. When the stronger opponents were beaten on the strength of four second- half goals, Galt had its first and only Olympic team sport champions. Indeed, the victory was Canada s first-ever team gold at an Olympic Games.

https://cambridgeshf.com/inductees/galt-football-club-1904/
http://www.canadiansoccerhistory.com/Great%20Teams/Galt%20FC.html