There is plenty of evidence, well documented, of how ancient Greek languages, and Attic in particular, sounded. Transliterations of Latin, Egyptian, Persian names, and words taken from other languages, and Latin transliterations of Greek names and words. Non-orthographic spellings and misspellings. Rhymes and the preservation of supersegmental qualities in poetry. Grammarians describing in detail how likely barbarians were to mispronounce certain words and how to best pronounce words. There's more to learn, but it's not unknowable.