GGG Ping.
A computer program...that seals it.
Betwixt 1.8 million and 10,000 year ago...that nails it down.
Psycholinguistics...correction, pycho linguists.
Nothing can be definitively known about the sound of Attic Greek (500-300 B.C.), a mere 2500 years ago for which we have both literary and introspective evidence, and we're to believe that an automated method will reveal what we can already guess--languages can have structural similarities because we, as humans, have a inherent capacity for language, independent of their vocabularies. Further, we were told languages evolve from highly inflected to word order languages, and experts are WAG'ing that this process oscilates between some speculated extremes.
This is not science. But such often appears in "Science" magazine.