The answer is simple once you understand that for thin-tailed distributions, the mean is way more important than population size for getting extreme results. In concrete terms, suppose that to win the olympics you need 5-sigma players (ones who are 5-standard-deviations better than the global average). Five-sigma players are extremely rare: a population of 100 million gets you about 25 to 30 of them. But now suppose you could bump up the quality of your soccer players until the average among them was raised just one standard deviation above the global mean. Now you only need a population of 1 million to generate the same number of five-sigma players. The end result: a tiny country of fanatics can compete against a huge country with tons of casual players, like the US.

You can "make" more fanatics under certain conditions. People respond to incentives, from the financial to the cultural to the brutal. I highly recommend the documentary The Two Escobars. It tells the story of famous drug lord Pablo, who used a portion of his fortune to bankroll soccer in Colombia, including the efforts of the national team. That national team included a defender named Andrés Escobar. In 1994, the soccer playing Escobar accidentally kicked in an own-goal during a critical FIFA World Cup match. He was murdered five days later, almost certainly by angry fans. That’s what a nation of hardcore soccer fanatics looks like.