An empire is a (supra-state) political organization that incorporates previously existing states. The formation of the U.S. empire occurred in America when the U.S. Constitution was adopted, because the individual 13 states gave up certain sovereign powers to the central government, the U.S.A., which was then the empire. In various places in the Federalist Papers, the essays explicitly mention this empire.
However, not all the i's were dotted and t's crossed. The question of secession was left hanging. This was resolved by force in the War Between the States, which I'd call the War of Union Ascendance. This war entrenched Washington as the governmental center of the empire. The empire is the United States of America, by which is meant the national government, not the country, people, nation, or land, whatever they might be or not be.
The U.S. government became an empire at its inception in 1787. There are very many commentators who say that the U.S. is not an empire. They are all wrong. They usually cite some irrelevant reasons pertaining to how this government behaves, saying for example that it behaves in a different way than past empires. Be such citations true or false, it doesn't matter. The U.S. was made an empire by construction at its birth. The War of Union Ascendance (1861-1865) actually is strong evidence that it was an empire and that the leaders of it intended to keep it that way. The Union was and is an empire. Since 1865, this empire has expanded and extended in various very obvious ways, making it ever more clear that the U.S. is an empire. Those who deny this usually have some political agenda in so doing. Thus, when Ron Paul and Pat Buchanan mention that the U.S. is too large of an empire, some who want the empire to expand will deny that their statements are accurate. Not all though. Others will accept this characterization and call for the empire to act even more like an empire.