Well, he IS the emperor, he probably could have just teleported it there, crafted the vault with his mind and locked it there. The emperor did have some pretty snazzy powers at his command when he was at his prime, he's been depicted doing this such as stopping time and having immense precognition powers before, but people often think less of it due to him being beat up by Horus.
The whole reason he got manhandled by horus was that he was holding back till the very last moment, and the fact horus was actively empowered and protected by the combined might of the four chaos gods. So it was effectively Horus + All of chaos VS Emprah by himself, with the worst possible outcome.
The Emperor is more or less a daemon prince in a sense (heresy I know). He's insanely psychic, can alter his appearance at will, and lives forever. If he's like the shamans that created him, he could reincarnate and come back from the Warp. He's a being of the Immaterium, rooted and tethered to the Material world.
Plus the thousands of psykers daily for ten thousand years part.
Pretty much this. In the 40k universe, only very few things can be called "beings of the materium" in the truest sense of the expression. Only stuff like the necrons, the c'tan and people with the pariah gene have no warp presence. Pretty much every living being has some sort of presence in the warp, and the emprah has been established as being more of the warp than of the materium since his birth, as he had such a massive presence in the warp he could actively protect imperium through the webway by essentialy making it part of himself, and his half-dead soul-shattered self is still actively arm wrestling the entirety of chaos away from the solar system and beyond.
Hell, even the primarchs are described as essentialy being partly warp beings, essentialy the emperor's own daemon princes. This explains some of the weird powers some of them are described to have, like, Leman Russ changing size as he goes into battle, Magnus changing his appearance to appear less threatening at the council of nikea, Sanguinius being space jesus and connected to every blood angel, etc.