I know there have been years of discussions about Evangelion's timeline. I've seen both the dates in the draft script for episode 4, and the dates in Rei Ayanami Raising Project.
However, the only pieces of information I recall getting in the show and EoE are:
The general timeframe of the sign in episode 2, placing episodes 1 and 2 in August 2015 at the latest. Up to interpretation based on how close construction was to completion though, it could be any time from January to August theoretically.
Also in episode 2 Gendo stated that Rei would be out of the hospital in 20 days.
Asuka's first day at school at the end of episode 8, and the most specific date given, as September 21st. Below the day supposedly even specifies Monday, which coincidence or not was the same for real-world 2015. I have not seen people talking about the day though so correct me if I'm wrong.
The re-match against Israfel taking place on a Friday 11th of an unspecified month, which can't be September given above. I assume October given the remains of Ramiel are still shown earlier in this episode.
Shinji's 30-day stint in Unit-01 in Episode 20.
And finally, Maya's laptop confirming that the events of EoE still take place in 2015.
The Evageeks wiki page here supposedly states that episodes 25 and 26 take place in 2016, presumably New Years' Eve/Day, but I might've missed it if this was the case.
The second and third points alone make it impossible to take place in 2015 with the real-world calendar system, given the 11th of October was a Sunday, and if it was December 11th it's impossible for the rest of the series to still take place before 2016. To make the October 11th date work, September would have to be 28 days.
I could end the discussion here technically, but now I want to speculate on what it would take to make this possible in-universe. The first thing that comes to mind is that Second Impact changed the axis so Japan was in eternal summer, so maybe it could have also changed Earth's orbital period, and the calendar for the years post Second Impact were changed to reflect this.
I thought about up with a modified calendar for fun, but if one cared about accuracy to when the previous years started and ended it would probably take a while, much less guessing specific days when major events like angel attacks happened. If I ever made some kind of fanwork where that would be important I'd probably just skip the hassle and use the Rei Ayanami project dates honestly.
Overall it's crazy that the main events of the series could have taken place over 4-5 months or so. Asuka's complaint in Magma Diver about not being able to find out when the Angels will attack is slightly less believable in my opinion, considering the average would probably be every 2 weeks or even less lol.
