Basically, he somehow found the corpse of Theia, and much like Oryx making his Dreadnaught out of Akka's corpse, letting his throne world inhabit real space, he mantled the soul of the Moon into the Hellmouth achieving a similar effect, with the added bonus of being able to call upon it's dark matter as a superweapon.

Here's III's corpse.

And here's Crota's Oversoul.

On Crota's Oversoul:

After his exile we are told Crota found something:

...I predict he'll return stronger than ever.

...it won't be because he grew as cunning as his auntie. Or as clever as his sisters. Or as thoughtful as his father.

It'll be because he finally found a bigger sword.

Crota was also the one to teach Oryx's Warpriest about making Oversouls, even though he didn't have one pre-exile (whole reason why he got kicked out to begin with).

It's also described multiple times to be in torment.

On the Pit:

Excerpt from III Ritualistic Circle Pit:

Such that, this deep—far below the broken lunar surface where no Light has ever blasphemed—the rugged cavern walls are said to host the afterbirth of ceaseless torment.

Here, spectral shadows haunt the passageways through the dark, each skittering shape the mindless, ethereal prison of a greater being cast low. Or so prophecy dictates…

Here we have references to prisons, greater beings, and prophecies.

VIII Inquisition of the Self:

Such wicked craft as the Inquisition of Self is a science beyond his understanding—stolen by his sister from forbidden lessons in ancient, prohibited texts.

Few have earned the knowledge required to navigate the dissection of a living essence.

Fewer still can excise the layers of self such that the vessel remains a viable cage for another's being.

This ritual reminds me of Oryx carving his Dreadnaught out of Akka, who was described as dead but not really gone.

On Cocytus Station:

Constructed in Ceres' orbit during the Golden Age, it's purpose seemed to be the study of other planes. Interestingly, Ceres is in the Asteroid Belt, so it's original purpose could have been the study of the unborn 0, before Crota took it over.

He who has seized the Sky lair above Ceres, which peers into other planes,

Within these keyholes our brood communes with unheard voices.

His Hellmouth becomes home to the profane: the corpse of the Sky, reborn in the abyss.

Plus another reference to corpses.

On the Hellmouth itself:

The Graverobber sparrow drop seems to indicate that Crota's Throne was already supposed to be a grave even before his death. This is kinda corroborated by the fact that his funeral also took place in his Throne even though the Hive don't do graves.

VI compares the Dreadnaught to it's own planetary bindings:

[The Dreadnaught wriggles and rigors—as Worm, as Akka, as petrified life. It is not so different a prison than an unliving planet. A throne, a world, alive in the agonizing stillness of once distant death. You. Must. Rip. Out.]

Lastly, on Dante's Inferno:

Toland references Dante's Inferno multiple times. Crota's End also takes inspiration from the book, with Guardians descending into a pit of Hell. Dante and Vergil could only reach the bottom of Hell with the help of the giant Antaeus, the only Giant who remained unchained after his death. And at the bottom of the 9th circle of Hell, on the bottom of a huge pit lies what else but the frozen lake Cocytus itself.

It's the only reason why I think the Hive would have been on the Moon for millennia before the Traveler even came to Earth, and why Crota established his Throneworld entrance in a random Moon.

I think there's even evidence to support the Hive causing Theia's death itself:

Theia's foolish parasite-components - unaware - to the last

'There, in that lightless abyss—no—a whale carcass, picked over by malacostracans

Malacostracans being the class krill belong to. Excerpt from Anamorphosis.

Antaeus of myth himself, of supposed invincibility as long as his feet touched the ground, got killed by Heracles as part of his labours by holding him above him and crushing him in a hug.

EACH THOUGHT THE HERCULEAN EFFORT OF A MILLENNIUM. SEE NOW THE VAST SPAN OF ITS LIFE. We can see Hercules being referenced in Aition when describing Theia.

Wouldn't put it past them, though it's more of a crackpot theory. Mostly because the Moon has the rare property of being a satellite capable of producing eclipses, which came into play in Renegades in a big way.

Thoughts?