I think it pre-dates the Republic. The very foundation of the Colonies were examples of British Imperialism. The popular version has Puritans founding the colonies in New England to escape religious persecution, but a quick look at a time line will demonstrate that Virginia colony was really the first colony (the story needed revision after the War of Northern Aggression). The French & Indian Wars were about colonist expanding into territories held by the Natives and their French allies.
One cause of the independence movement was the Brits banned settlement further in the west. Shortly therafter the first in a series of shady land deals started the westward expansion. Napolean conquered Spain, installed his brother as king and sealed the deal for the Louisiana Purchase. We sent the dough to the Bonapartes' to support THEIR expansion efforts. And so it went. Jackson was a notable imperialist being very big on ethnic cleansing (see Trail of Tears). And so it went with the siezure of Alta Mexico and a brief stop at the western edge of North America.
McKinley made our first Far Eastern adventure 1n the late 1890's with the war in the Phillipines. An early Guerrilla conflict that resulted in heavy American loses, which we no longer talk about. We made a stab at China in the early 1900's, sending Christian Missionaries to be followed by American merchants and of course, American military to protect our citizens. Unfortunately, the Chinese had seen this game before. They slaughtered the missionaries post haste and our military never made it to save the day. And we all know the rest of the story.