@Agnaa
"Gilman decided he had picked up that last conception from what he had read in the Necronomicon about the mindless entity Azathoth, which rules all time and space from a curiously environed black throne at the centre of Chaos."
Then you have the "ancient legends" of The Haunter of the Dark, which come from the protagonist reading the Necronomicon and other such dark tomes.
The reason most people know about Azathoth, just like Yog-Sothoth, is because of the Necronomicon. The exact same Necronomicon which refers to Yog-Sothoth as containing past, present, and future refers to Azathoth as the being who "rules all time and space" and as "Lord of All Things".
Again, the Necronomicon is fractional, but suggests Azathoth to be at the top, which Lovecraft did, as well.
The issue with putting Yog-Sothoth somewhere above him is that it is not backed by any actual statements in-universe (Azathoth is never mentioned in TtGotSK) nor author statements (the single comparative thing we have between them from Lovecraft places Azathoth higher).
If this is more an issue about "none of these quotes mention the Supreme Archetype", I will again mention that the Supreme Archetype is Yog-Sothoth; every name used to refer to the same creature in TtGotSK is written in all caps. "YOG-SOTHOTH", "BEING", "ENTITY", "PRESENCE", "SUPREME ARCHETYPE", etc.