There must have been some non-Americans who contributed at least indirectly... maybe who helped develop the technology in earlier phases?
Well, the man in charge of developing the Saturn V rockets that brought the Americans to the moon was Wernher von Braun, a German who had been in charge of Nazi Germany's rocket programme during the war. In fact a lot of the people he had worked with during the war ended up at NASA.
There were several dozen Canadians and Brits who joined the US space program after the Canadian Avro Arrow jet fighter (reputed to be one of the best aircraft of its day) was cancelled. These experienced managers and engineers filled many important positions and contributions. One example, Chamberlin, was a project manager for the early Mercury and Gemini, before becoming a systems engineer / troubleshooter for Apollo on the capsule side.