Is there any possibility where one can find the Stack Exchange Network deep within the Permafrost layer?
Not sure if the Internet Archive is deep and cold enough for you, but the company does quarterly data dumps at: https://archive.org/details/stackexchange
But if you want more, there is an organization called the Archive Team that has dedicated itself to doing such things. They might start archiving the whole of the Stack Exchange Network including images and other stuff for good if such a project were proposed. A quick search on their site returns no active project in this regard though.
And there are obstacles too (as there are for Github, I doubt they archive private repositories for example). The site design here is property of the company and one would need permission from them before archiving. Even worse, the linked and included external content is probably all sorts of mixed copyright. I'm not a lawyer, it may all be harmless, but I can also foresee legal problems there.