It's okay to put questions up here.
I'm writing that, because I just received another inquiry about classical music via PMs. Really, I don't think putting a question in a thread like this implies any special ignorance. Gods know, it's an area of specific interest and research. It's not like asking the number of current oceans in the world, or the number of planets in our solar system.
So to the question: how far back does classical music go?
It depends on how you define "classical music." If we decide we mean symphonies and quartets, then roughly 1725 is a good starting point: both those forms were then in evolution, the quartet from the French/Italian sonata a quatre, the symphony from the triparite overtures to Italian operas. But if we allow madrigals, masses, and other secular/sacred vocal music, we drop back at least to 1400 AC.
The troubadours and trouveres are typically classified as "classical." That takes us back to the 13th century, after the French and Teutonic musicianly aristocrats experienced a cultural revolution after contact, during the Crusades, with MidEastern Islamic civilization.
And if we then include very early Roman Catholic Church music, we could probably push things back to 1100 or so. There are references in a couple of texts, as well, to polyphonic music existing as early as 900, though the music is largely lost. (Music was preserved in a much more basic form, minus such aspects as rhythm, for hundreds of years.) So most musicologists declare that classical music starts around the beginning of the 13th century, with the troubadours/troveres, and with the Notre Dame school of sacred composition.