The first seven lines of the Iliad are:
Μῆνιν ἄειδε, θεά, Πηληϊάδεω Ἀχιλῆος οὐλομένην, ἣ μυρί᾽ Ἀχαιοῖς ἄλγε᾽ ἔθηκε, πολλὰς δ᾽ ἰφθίμους ψυχὰς Ἄϊδι προΐαψεν ἡρώων, αὐτοὺς δὲ ἑλώρια τεῦχε κύνεσσιν οἰωνοῖσί τε πᾶσι· Διὸς δ᾽ ἐτελείετο βουλή· ἐξ οὗ δὴ τὰ πρῶτα διαστήτην ἐρίσαντε Ἀτρεΐδης τε ἄναξ ἀνδρῶν καὶ δῖος Ἀχιλλεύς.
I ran across an interpretation that was new to me, which was to read line 6 as modifying "Μῆνιν ἄειδε," so that the muse is being asked to start the story from a certain point in time. This is in a short translation by Hartsock of a few passages, https://exchanges.uiowa.edu/issues/traces/iliad/ (Her translation has some odd features, like the use of homophones for the sake of being homophones. See her translator's note.)
Menace – sing to us, goddess, the menacing rage of Achilles, son of
Peleus, that rained a thousand agonies down on the Achaeans, and sent
so many noble souls of heroes down to Hades, and delivered to those
noisy crows and dogs the spoils of their bodies.
And thus the will of Zeus was, as usual, fulfilled.
Start your song here, when they first stood apart in their quarreling:
the son of Atreus, lord of men, and shining Achilles.
On the other hand, Butler has:
Sing, O goddess, the anger of Achilles son of Peleus, that brought countless ills upon the Achaeans. Many a brave soul did it send hurrying down to Hades, and many a hero did it yield a prey to dogs and vultures, for so were the counsels of Jove fulfilled from the day on which the son of Atreus, king of men, and great Achilles, first fell out with one another.
So here this line is taken to be a description of when Zeus's plans begin to be fulfilled. Stanley is similar, although he takes it as a description of when the plan was "decreed."
Chapman has this:
To all which Jove’s will gave effect; from whom first strife begun Betwixt Atrides, king of men, and Thetis’ godlike son.
This is pretty similar to Butler in that it refers back to Zeus's plan rather than the muse's song, but it eliminates the reference to a point in time and instead translates ἐξ οὗ as "from whom."
Yet another interpretation by Cowper:
And Heroes gave (so stood the will of Jove) To dogs and to all ravening fowls a prey, When fierce dispute had separated once The noble Chief Achilles from the son Of Atreus, Agamemnon, King of men.
So here, the "from" is only incidentally about time, doesn't relate to Zeus or the muse, and is simply a causal connection, saying that the interpersonal dispute was the cause of the woes. Pope gives a similar time-and-cause interpretation, but more explicitly connects the strife to both the woe and Zeus's plan.
These all seem to be variations on the same theme, except for Hartsock, whose interpretation is completely different. Is there anything that can be said objectively about the meaning of the text?
I have a hard time understanding all the nuances of many of the little particles in Homer, but it seems to me that if δὴ here means "truly" or "indeed," then it's hard to reconcile that with Hartsock's reading. It makes more sense to say, "Truly his fate was sealed when he started drinking alone..." than "Truly, start singing Happy Birthday from the second bar..." However, the commentary by Anthon says that here δὴ means "a precise point of time."
Logically, I don't see the need for line 6 under Hartsock's interpretation. In her interpretation, the poet is saying, "Sing about the rage of Achilles [which had these results according to Zeus's plan]. Sing starting when the rage began." This is sort of redundant. We're leaping into the story in the middle, so it makes sense in a preamble to explain why we didn't start earlier, at the logical beginning, with Helen's abduction. But if we've already asked the Muse to sing to us about the rage, then it's redundant to say that we can't start earlier than the rage began.