It would be whatever is played by the Brits as they can seed it across most of the world in the 19th century that probably rules out handball as it is eurocentric/germanocentric and quite late - rules are 1906 according to wiki so all the railway staff in South America would have been playing something else for 20-50 years anyway.
And pre plastics it would need a case ball or something that does not need to bounce much. (volleyball with a pigs head, not so much)
Football, with the biting and gouging, is ancient or at least medieval so the betting is on Rugby like handling/kicking game (which pre dates soccer) but that could be Union, League, Gaelic or Aussie rules.
Smaller chance of a hockey/hurling/lacrosse game because you need more kit,
Still smaller chance of Cricket for the same reason and weather and time but it does stand a good chance of being a summer sport.
Baseball is cricket for people who can't bowl and American football is an equipment heavy rugby derivative.