Well, supreme archetype isn't a trope/archetype in fiction like true hero or dark lord. It is a formless undefinable being in Cthulhu Mythos and all outer gods are fractions of it. In this wiki we used to take azathoth as the supreme archetype but the description of supreme archetype makes it crystal clear that azathoth isn't exactly the supreme archetype and even azathoth seems to be mere fraction of it.
I am working on a blog that'll explain these things. For now I am adding the supreme archetype in the omnipotence page.
Yog sothoth has been described as an incomplete facet of supreme archetype. When people think about suprem archetype, they thing about yog sothoth because it is all in one and one in all but in reality as stated in the short story, it is just merely an incomplete view of suprem archetype.
"It was an All-in-One and One-in-All of limitless being and self—not merely a thing of one Space-Time continuum, but allied to the ultimate animating essence of existence's whole unbounded sweep—the last, utter sweep which has no confines and which outreaches fancy and mathematics alike."
All the outer gods are mere facets of Yog-Sothoth.
Again, it's been stated that Yog sothoth is an incomplete view of Supreme archetype in the through the gates of silver key. My blog will contain the actual scans and statements. So, have some patience.
Read through the gates of silver key short story, it contains everything.