Listen up humanity, I hate to be the one to tell you this, but we only have a scant few hours before we're all turned into a giant ocean of orange goo. There's probably going to be some radical robot/monster/monster-robot fights happening around you, but don't worry, no matter how freaky those things look it won't matter because as I've previously said, we're joining that sweet goo pile made of people. Also, though there is a giant naked girl rising to the heavens, please do your best not to stare, she's like 15, or a clone or whetever, either way it's gross.
The point is we've reached December 31st 2015 - January 1st 2016 the time most Evangelion fans agree is the date of the Third Impact event.
Though there is no "official" dates in the series, the anime does move linearly through time and specific holidays like Christmas and school breaks are followed in a straightforward fashion. One of the hallmarks of the series is how each character changes after going through so many harrowing experiences. According to sites like the Evangelion Wikia and QMisato the key piece of evidence for the New Year's Eve - New Year's Day claim is that the final events of the anime series are taking place in late December of 2015, while a computer screen in the End of Evangelion movie specifically lists year as 2016. Meaning that the events of the Third Impact took place over the course of New Year's celebrations.
The Evangelion saga is an important hallmark in the history of anime, even at its most navel gazing extravegance it took the language of action shows and made it about something more. There's a reason why "Shinji, get in the robot!" is nerd shorthand for "grow up and accept the emotional pain and sacrifice of adulthood".