What is the first attested use of 美國/美国 in the sense of 'America' in Chinese?

Question

The beginnings of Sino-American relations date back to the late 18th century (e.g. the Old China Trade). When did the Chinese begin to refer to America (or the US) as 美國/美国? Were there alternative names referring to America/US?

Answer 1

There were more than 10 names for USA in history.

• 亚墨利加国, after 1776;
• 花旗国, after 1784;
• 咪唎坚国, after 1784;
• 咩哩干国, after 1820;
• 亚美利加兼合国, after 1833;
• 弥利坚国，即育奈士迭国, after 1836;
• 美理哥国, 美理哥合省国, 美理哥兼摄邦国, 1838;
• 亚美利格合省国, 1844;
• 亚美理驾会邦国, 1844;
• 亚美理驾合众国, 1844；
• 米利坚合众国, 1848;
• 大亚美理驾合众国, 1858;
• 大美联邦, 1861;
• 大美国, 1901;
• 美利坚合众国(美国), after 1902;
• 美利坚合众国, determined in 1913;

Reference: “美利坚合众国”译名的由来

Answer 2

Before that, the name apparently stuck from Mateo Ricci's (Li Zhizao and Zhang Wentao) map. As you can see on the map, first name tagging was purely phonetical, drawing from "America", which in turn was taken from Americo Vespuccio instead of from Christopher Columbus (Cristóbal Colón, whose name as discoverer of the continent was used to name a single country only: Colombia) for diverse reasons, including the "Black Legend" that other colonial powers spread against Spain's preponderance at the time. Noticeably enough, Spain's name was also different in Jesuit Mateo Ricci's map, being read "XiBaNiYa" (西把你亞) instead of current "XiBanYa" (西班牙), with a character ('亞') other than the "tooth" ch. ('牙'), but homophonous, apparently to indicate its southern location and homeland character.