When Does the Second Remake of "Godzilla", "Shin Godzilla" (2016), Take Place?
"Shin Godzilla" (released to English-speaking audiences as "Godzilla: Resurgence" and Swedish-speaking audiences as "Godzilla: The Return") is an adventure horror (kaiju) film written by Hideaki Anno [remaking "Gojira" (1954) by Takeo Murata with IshirÅ Honda] that released July 29th, 2016. So when is "Shin Godzilla" set?
It takes place in the year:
We know this because almost a third into the narrative when the government officials first make the connection between heightened radiation levels and Godzilla's path through Tokyo they look to the online social media platform Twitter and see that radiation-tracking hobbyists among the public have already made the connection. Its logo is clearly visible. The social media platform Twitter publicly launched on July 15th, 2006 AD so it must be after mid July of 2006 AD.

2023 AD
We know this because almost a third into the narrative when the government officials first make the connection between heightened radiation levels and Godzilla's path through Tokyo they look to the online social media platform Twitter and see that radiation-tracking hobbyists among the public have already made the connection. Its logo is clearly visible. The social media platform Twitter publicly launched on July 15th, 2006 AD so it must be after mid July of 2006 AD.
More specifically, it’s theorized that Godzilla is created by a marine animal ingesting illegal radioactive waste in Tokyo Bay and when the photographic "documents" are shown to the government officials, they say, "This is 60 years ago." The earliest that radioactive waste has been produced in Japan is 1963 AD, when the Japan Power Demonstration Reactor, an ongoing nuclear reactor test began operating. So the earliest the story can take place is 2023 AD.
1,963 + 60 = 2,023.
Specifically, at the very beginning of the movie when the Crisis Management Center gets some aerial footage "Nov" is visible at the bottom-right of the screen and, later, a short bit of faux found-footage taken by a civilian is timestamped "11/03". Closer to a quarter into the story, a document at a meeting is dated for "November 5th" and specifically refers to Godzilla's emergence as at "Around 8:30 AM on the 3rd day of the 11th month". So the story certainly takes place in November (possibly of 2023 AD).
It can be retroactively absorbed into the MonsterVerse Universe at a chronologically early spot (a first chronological film to feature Godzilla).

