The United States can have a powerful economy because they can create Settlers faster than other civilizations since like the British they spawn settlers whenever a Manor is built.
The United States military is very powerful especially later on in the game because their Musketeers and Hussars, two mainline units, can be upgraded to Royal Guard level. However unlike the British they train Skirmishers instead of Longbowmen and can also train rockets from their Artillery Foundry and Heavy Cannon from their Factory. They are unable to upgrade the Heavy Cannon with the Imperial upgrade, which instead is only available to their Rockets.
The US Flag show in the original game for campaign clearly has 24 stars, placing the events of Act III between 1822 and 1836. Which is far earlier than both Major Cooper's involvement in the Mexican-American War (1845) and even the start of the construction of the intercontinental railroad in the mid 1840 to the late 1860s.