Translations of the Greek New Testament into other ancient languages help us know what the sounds were in ancient Greek compared to now. In order to translate Christian texts, the Copts invented 7 extra glyphs for sounds unknown to the Greeks, but which they needed for their language. This is informative to us as to what Greek sounded like as late as the early church times. Thus we know that even as late as the Christian era in Egypt, the Greek letter φ (Phi) was not pronounced like English “F” but instead like our English “P.” We know this because Coptic had to invent a separate letter Ϥ for the F sound, a sound which Coptic had, but Greek did not have.
And because of the law of Phonetic symmetry in the distribution of points of articulation in the mouth, we can reasonably extrapolate this principle to the other set of consonants also, that is, Χ and Κ. And predict the following: the Greek letter χ sounded like our English “K” and the Greek letter Κ was a softer, unaspirated K for which English does not have a letter or symbol. In Phonetics we find that languages that have both an aspirated and unaspirated P, will also have both aspirated and unaspirated versions of the other stops such as T and K etc. Thus, φ was p sound, θ was t sound, χ was k sound, and π, τ, κ were unaspirated versions thereof, for which we do not have letters in English.
Another example that Plumley gives in Metzger’s book shows that the Greek letter θ definitely was not a “th” sound like we have in English, as in the word “thick.” It was simply our Englsih “t” sound, as in “tick.” One way we know this is because Coptic translators, when they heard the Greek word θαλασσα, wrote down HALASSA with the feminine definite article T in front of it. That’s because it was pronounced TALASSA and the scribes or translators heard TALASSA.
The above knowledge can lead us to some interesting insights. For example, knowing that φ was pronounced “p” and θ was pronounced “t,” we can pronounce correctly the word φθινοπωρινος in Jude v. 12, and recognize our English word “patina” there, and see how that relates to change in color of leaves in Autumn. Greek had a word φθινα for the mildewing of material (which would change its color), but see also φθῖνάς “a waning, a wasting away”, or φθινιασμα “declining,” and the verb φθινω, “to perish, decay, waste away.” Our English word patina also refers to the wasting away or corrosion of semi-precious metals, like copper and bronze, upon which a green film accumulates.
This page gives the correct pronunciation of ancient Greek consonants.