Besides the testimony of sources like Herodotus, we have early examples of Greek alphabetic writing and examples of Phoenician writing, and it's beyond question that the Greek alphabet is derived from Phoenician (or some closely related system).
The Hebrew alphabet was similar--for the Hebrew letters see Psalm 119 which has 8 verses for each letter (aleph, beth, gimel, daleth, he, vau, zain, cheth, etc.). The present-day Hebrew letters are written a bit differently, since they use the Aramaic letters. The oldest Greek letters are closer to the Phoenician letters in appearance, and were written from right to left. The Greek letter names are clearly derived from the Phoenician names, and the order of letters is almost the same (the Greeks made some minor changes, and created a few new letters).
Greek is one of the so-called Indo-European languages; the ancestral language (which English, Latin, Armenian, Celtic, Persian, Russian, Hindi, and many other languages are ultimately descended from) is called Proto-Indo-European (or PIE). The date when PIE was spoken is not exactly certain, but was probably later than 6000 B.C.
Yes, I'd entertain both of those hypotheses before the hypothesis that it's the Greek alphabet, unless there's additional evidence beyond that potsherd. Perhaps if they ever decipher Linear A it will shed additional light on the prehistory of Greek. Linear A has a character that looks like somewhat that Upsilon/Delta character I mentioned--see for instance left-hand pic, second row, third character from right:
