"For verily there are gods, and the knowledge of them is manifest" (Letter of Menoeceus: Hicks translation).
And further questions came up for me, including the how to imagine why it might be that Epicureans held the gods to be important.
From Wikipedia "Ancient Greek Religion" "Ancient Greek theology was polytheistic, based on the assumption that there were many gods and goddesses, as well as a range of lesser supernatural beings of various types. There was a hierarchy of deities, with Zeus, the king of the gods, having a level of control over all the others, although he was not almighty."
Here is a website listing and describing the Greek gods (Olympian Gods, Titan Gods, Primordial Gods, Sea Gods, Underworld, etc.) https://www.theoi.com/greek-mythology/greek-gods.html
1) There was a common understanding of gods in ancient and hellenistic Greece
2) Epicureans saw the gods differently than what was commonly held - as not concerned or involved in the lives of humans, and as not something to fear.
It came to me that maybe the work of Jung or Campbell could help make sense of things -- specifically the idea of "archetypes". I've tried to find an online article which might explain the Jungian understanding of Greek gods, but haven't found one. (Joseph Campbell took the work of Jung further, and somewhere within his four volume book "The Masks of God" it might have something on Greek mythology - but will need to see if I can find it at the library.)
So to explain archetypes -- I pulled out my book by Carl Jung "Man and his Symbols" and on page 67 on The archetype in dream symbolism -- there is not a clear direct explanation so I will attempt to synthesize and explain:
---The mind (psyche) still has "archaic remnants" left behind from our earlier time of development in archaic man whose psyche was still close to that of the animal. These "archaic remnants" are what Jung calls "archetypes" or "primordial images" and these archetypes come to us through dreams.
----"The archetype is a tendency to form such representations of a motif---representations that can vary a great deal in detail without losing their basic pattern."
----"They are, indeed, an instinctive trend, as marked as the impulse of birds to build nests, or ants to form organized colonies."
And now to make sense of the Greek gods -- that these were reoccuring archetypal images that came through dreams.