Ancient Greek is outside the scope of our forum, our expertise is in modern Greek.
I asked an archaeologist and still he could not give a definite answer:
I am certainly not an expert, but my understanding is that diacritical
marks were not used in written Greek until well into the Hellenistic
period as can be seen, for example, in the Derveni papyrus. (accents
were certainly known in the oral language and that must be the origin
of the later diacritical marks.)
Epiktitus lived at a time (1st AD) when written marks were certainly
known, but I do not know if they were used by authors in composing, or
exclusively by grammarians-librarians.