Who invented classical music?
Like all the arts (theater, painting, sculpture, literature) "classical" music wasn't "invented" - it was just .... music, which developed as part of the cultures in the world. The label "classical" (which has at least two meanings and more) came to be put on the music of the era from J.S. Bach to Beethoven at some time in the 19th century, but now it refers to either the "common practice period" (from about 1550 to 1900), or, more specifically, the work of the "classical" period of European music history from about 1750 to 1825 or so (following the "Rococo" and followed by the "Romantic" periods).
That isn't to say that there are characteristics of this music that weren't "invented" but it's more of an evolution, probably from 11th century (the effort to create a written notation) on. I guess if you want a name, try Guido d'Arezzo back then, or a better known name, try J.S. Bach. Neither one was especially "inventive" but music notation could be said to date from Guido's time whether he "invented" the idea or not, and the music we listen to almost exclusively as "classical" music never dates from before Bach's time.
No one really "invented" classical music. The term ‘classical' is a bit ambiguous when it comes to music. It can refer to music that shows its roots in traditional Western culture, or it can refer to the ‘classical period' of music which ranged from around 1730–1820. Prominent composers from the classical period included Mozart, Haydn, Giordani, etc. Music is an ever-evolving aspect of culture. Different time periods of music (Renaissance, Baroque, Classical, Romantic, Experimental, Contemporary) were all times where composers and performers worked through new rules and new limitations (or lack there of).