Some people believe that America as a name stems from the mountain range known as Amerique located in Nicaragua. All of this is before America first appeared as a name on the mainland roughly in the area of Venezuela. Most of us have probably been taught that America as a name is derived from that of Amerigo Vespucci, a notorious liar and enslaver of Native people. From the early 1500's until the mid-1700's the only people called Americans were First Nations People. Similarly the people called Mexicans, Canadians, Brazilians, Peruvians, etcetera, were all our own Native People.
English usage is very little different.
Nonetheless, beginning in the 1740's-1780's British newspapers also began to refer to their British subjects on the Atlantic seaboard as Americans in the sense of Britons living in America. After the United States became independent in the 1780's its new citizens began to refer to themselves as Americans, trying to identify with Tammany and the Native People. It is simply nonsense to refer to the United States as America.