Final answer:
Considering the Monroe Doctrine and historical precedents, the likely position of the United States would be to protest and potentially take diplomatic action against Great Britain's occupation of Argentina in 1830.
Step-by-step explanation:
If we consider the historical context of the early 1800s, particularly in 1830, one might predict that the United States would likely protest and possibly take diplomatic action against Great Britain if it sent troops to occupy Argentina. This stance can be surmised by looking at the principles set forth in the Monroe Doctrine, which was a cornerstone of U.S. foreign policy that warned European nations against interfering with independent nations in the Western Hemisphere. This doctrine was established in part to prevent European re-colonization of Latin America and to maintain economic and political influence in the region. Moreover, historical evidence suggests that when faced with the potential European intervention in Latin American affairs, the United States, coupled with British commercial interests, was inclined to oppose such actions.
Therefore, the most likely position for the United States, given its own doctrines and previous actions in similar circumstances, would be option A) The United States would likely protest and possibly take diplomatic action against Great Britain.