I believe the first Chinese "machine-struck coinage" (this is the usual terminology used by numismatists to distinguish modern Western-style coinage from traditional Chinese cast cash coinage) were the "Old Man Dollars", struck for use on Taiwan. However, if you're hoping for specifics about dates and places for these coins, then sorry, we can't give them - these early Chinese dollars are very unclear about how, when, where and why they were made, or even how "official" they really are. They appear to have been made sometime around the late 1830s and the earliest records of their existence date to 1841. The name "Taiwan Arsenal" appears on them in big, bold Manchu script and the city of Chiayi on Taiwan is named in the Chinese script, and there seems to be some evidence of their actual early use on the island.
Don't say "infinitely" when you mean "very"; otherwise, you'll have no word left when you want to talk about something really infinite. - C. S. Lewis