The Ionian scale is the major scale, which is one of the two most commonly used scales. (As the remaining five are rare compared to) It is far the most commonly known, and it is being even used in these kinds of works. So I have a question: when was the Ionian scale invented?
The Greek modes go back as far as Pythagoras, so 500-600 BCE.
However, while the modes included many of the modes that are familiar to us today, the Ionian and Locrian modes did not actually exist back then. The Ionian mode came about in 1547, devised by a music theorist named Heinrich Glarean (the name is made up and has nothing to do with actual Ionia). The Locrian mode is older, but didn't get used much due to its lack of a perfect fifth above the root; in modernity, its common use is in jazz, to melodize over diminished chords.
You can't really put an exact date on it, but documented history of Ionian and the other modes goes back to plainchant. That's from the dark ages, around the year 900 AD.
The history of modes isn't a very linear and neat process, so it's not necessarily easy to pinpoint an invention date. The YouTube channel Early Music Sources has a good video on the history of modes where the talk about the various historical theories of modes and their names (the ionian is first mentioned at around three minutes in). The video description has a link to further sources if you want to dig deeper.