They were the first organized football club in the United States.
Different people have different answers to that question.
All of them sincerely believe that they are correct, although they can't all be. Personally, I believe that we don't know the answer, and probably never will. Some people take the idea that the Oneidas were playing soccer and that this was the birth of the sport in the United States almost as an article of faith. I have heard one such advocate contend that if you fed various data about the Oneidas into a computer, like the computers that have been used to determine the results of hypothetical boxing matches between champions from different eras, it would unquestionably spit out the answer that the game being played was soccer. My view is that this is not the proper way to study the past.