The way I see it working now (after ditching my flawed understanding), it’s like a boolean flags for “first” effects. When you make the first successful run on archives, that flag gets set false after all effects relying upon it occur. Replacement effects will not reset the flag; sneakdoor won’t retroactively turn on the “first archives success” flag, despite that there was no successful archives run after sneakdoor fires.
So pretty much what Kesterer said, except instead of “was there a first successful run on archives”, I’d say “is the first archives flag set”. Difference being the later doesn’t make it sound like archives was successfully run (first or ever).
And that’s admittedly a pretty pedantic difference given the current card pool, but I feel like if there was a card that said “Play only after your first successful archives run”, you wouldn’t/shouldn’t be able to install it after a sneakdoor run (but that’s more design level than rules-querying level, and is moot for the current pool anyway).
So archives would be my answer for the apocalypse question (which lines up with the accepted answer). But this is also after hastily re-evaluating my position after proving myself wrong. Maybe that isn’t correct (WRT my reasoning; archives is definitely the answer to the question).