Until the European discovery the America’s had no seafaring nations and the original inhabitants of North- and South America suffered greatly due to western greed, expansionism and diseases.
In 1750 South America has been colonized by Spain and Portugal for over 200 years. They carved up the continent into a collection of Viceroyalties and Captaincies, creating the nations as we know them today. They ran these nations pretty independently under Spanish and Portuguese overlords, and little trace of their former cultures or peoples remain.
Other western nations have an interest in the South American territories and a continual power struggle for territory is taking place, especially around the Caribbean sea where borders of different powers meet and a region of multiple islands makes it an ideal hideout for outlaws.
New Spain and Brazil are the largest nations of the region. If they can organize an uprising against their overlords they might be able to fight for independence, but they will need allies or a weakened Portugal and Spain to succeed.
In 1750 North America was settled for little more than a hundred years, but only on the east coast. Britain holds the Thirteen Colonies, which are divided into the Southern, Middle and New England Colonies. The declaration of independence came 26 years in the future, but perhaps the Colonies will aim to improve on this date. However, at this time the economic strength of the Thirteen Colonies is not great and the struggle will be hard, even if the Colonies manage to unite. To the north the French rule in Nouvelle-France, and they are wedged between the British Colonies and the British Hudson Bay Company, placing them in an uncomfortable position.
Due to numerous undiscovered lands and many ports with weaker defences, the America’s are an attractive region for expansion. It will be hard to predict which nations will come from the east or west to look for opportunities.