What year did the United States of America begin minting coins?

1792 was the year the US Mint began operations. The first official coins were half cents and cents made for circulation in 1793.

Other denominations followed over the next few years - half dimes, half dollars, and dollars in 1794, $5 and $10 gold in 1795, and dimes and $2.50 gold in 1796.

There were semi-official trial pieces made in 1792 but these did not circulate. Source: www.coinfacts.com