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