It's hard to be a superpower with 37 million people, but in 1900 Argentina didn't yet have 5 million. And in 1950 it hadn't reached 20. Uruguay was vrey rich in the 1950s, yet it had no influence in the world because it only had 2 million inhabitants.
However, the extent of the U.S. land mass is bounded in the west by the Rockies and the deserts of the Great Basin, so in reality, the amount of arable land that both countries started out with is comparable. The arable Argentinian Pampas is closer to the coast than are the plains of the U.S. Just as importantly, the rivers in Argentina flow East-West, whereas the U.S. have the Appalachians between the East coast starting point and the breadbasket. This gives Argentina a STRONG head start in terms of being able to easily populate and exploit the arable interior.
In this light, Argentina should have had a higher initial population than the U.S. did. Argentinian farmers didn't have to clear fields for rocks as did the farmers of New England. They didn't have to cross the Cumberland gap or clear trees for farms in NY.