Timeline #10: Adam's Apocalyptically-Abrupt Awakening...Averted!
*Ding!*
"Wait a moment...did I oversleep? And what's this-there's life already on this planet?...Very well-I'm outta here!"
It was there in 1998, before the Katsuragi Expedition was even a twinkle in its organizers' eye, that the being who would have been codenamed 'Adam the First Angel' used their godlike powers to teleport themselves out of the Antarctic ice they'd found themselves buried in. Their act transported them to the planet Mars, a more barren environment that proved to be well-suited to the creature's particular form of life.
Thus, with no 'Angels' on Earth to fight, and the Dead Sea Scrolls rendered effectively worthless, SEELE's plans for the Human Instrumentality Project, decades in the making, unceremoniously fell apart. As a result, the now-former masterminds who made up the cabal instead decided to spend their days idling around, wasting their vast fortunes away on the loosest women, the finest wine...and the purest narcotics imported from South America.
Neither the U.N. Artificial Evolution Laboratory, nor its successor entities GEHIRN and NERV, were formed; all those who would have been affected by the nonsense of the Second Impact catastrophe (which never came to pass) ended up living normal, somewhat unremarkable lives...
(Well, everyone, that is, save for Rei Ayanami and Kaworu Nagisa, what with their not having been...you know, born and all.)
The (mostly happy) End!