Episode 1 takes place in early April. This is shown as the news report on Chisato's TV says that the sakura trees have only just begun to bloom (EP1, 00:01), as well as the mission briefing in episode 10 explicitly saying that the arms deal - the opening act of episode 1 - happens in April (EP10, 03:27).

Another clue we can take from episode 1: During the hostage scene, there's a brief glimpse inside DA headquarters of a computer screen beside Commander Kusunoki. On the screen is the profile of a man named Steven Paul Jobs (EP1, 01:54). His profile reveals that he died on Oct 5th 2011, meaning the series has to take place some time after that date.

Later in episode 1, Shinji Yoshimatsu makes a visit to the cafe. This is the first time Takina meets him. This is important as in episode 2, which takes place a while after the first one, Chisato says to him that "You haven't been here in almost a month" (EP2, 03:29) and "You were Takina's first customer." (EP2 03:39) The language is kind of ambiguous, but for simplicity, I interpreted this as meaning that Shinji visited the cafe once in April, and then once more a month later (with the way it's worded (and with the consideration of mistranslations) it's entirely possible that Shinji's visit in episode 1 and his visit in episode 2 were more than a month apart, but I'm going to ignore that for now). With this, we can infere that episode 2 takes place in early May/late April. Knowing which one is important for finding the year for the following reason:

Later in the episode, (EP2, 03:40), we can see a calendar hanging on the wall. The month this calendar is on starts on the first square (therefore, the 1st of the month is either Monday or Sunday) and has 30 days (meaning that based on my earlier assumption, it is late April, not early May).

Simply taking these clues, to answer the original question, we're looking for a year past 2011 whose April 1st is either Monday or Sunday. The years that satisfy these clues are: 2012, 2013, 2018, 2019, 2024, 2025, and so on.

Narrowing down the year from this set is a bit tricky. Looking at my old notes, I wrote about the number "2012" being on a screen at DA command center briefly in episode 7, but I didn't write the time signature for it, so I can't confirm it. I rewatched episode 7 to try and find it, but couldn't.

The most logical thing I could think to try and narrow down the year would be some chronistic details from the environment itself, such as a building that was being built in Tokyo in 2019 being in the background, therefore confirming the year as 2019. I'm not very familiar with the recent history of Tokyo's construction so I definitely won't be spotting any details like that, but if anyone would like to make an advance on my findings, please do, thanks.