>>213102766
Do you have "math clubs" back when you were in high school? It's like that. They do math stuff in clubs. Then they enter into competitions for district, cities, states, then nation wide. The best performers are picked for a team. Then somebody would coach the best of the best, they were usually winners of previous Olympiads, or somebody who excelled in their field. They very likely do it for free, as a hobby, or they're there to scout talents.

Team USA's informatics coach is a billionaire himself who works for OpenAI, and he's likely there to scout for talent.