When Does "Pacific Rim" (2013) Take Place?
"Pacific Rim" is a science fiction adventure horror (kaiju) film written by Travis Beacham with Guillermo del Toro that released July 12th, 2013. So when is "Pacific Rim" set?
It takes place in the year:
We know this because early in the main action Marshal Stacker Pentecost says, "Long time." and Raleigh Becket replies, "5 years, 4 months.", referring to the time since they'd last spoken to each-other during a kaiju attack on Alaska in 2020 AD during the prologue. And when asked, "So when was the last time you jockeyed, Ray?", Raleigh responds, "About 5 years ago.", referring to the same 2020 AD event in Alaska. Furthermore, a title card superimposed over the footage at the start of the third part of the prologue reads "5 YEARS LATER ALASKA BASE - CLOSING DAY".

2025 AD
We know this because early in the main action Marshal Stacker Pentecost says, "Long time." and Raleigh Becket replies, "5 years, 4 months.", referring to the time since they'd last spoken to each-other during a kaiju attack on Alaska in 2020 AD during the prologue. And when asked, "So when was the last time you jockeyed, Ray?", Raleigh responds, "About 5 years ago.", referring to the same 2020 AD event in Alaska. Furthermore, a title card superimposed over the footage at the start of the third part of the prologue reads "5 YEARS LATER ALASKA BASE - CLOSING DAY".
2020 + 5 = 2025.
More specifically, Pentecost's other early line: "I've spent the last 6 months activating everything I could get my hands on." implies it has been 6 months since the final prologue scene labeled as "ALASKA BASE - CLOSING DAY". This means it is mid-to-late 2025 AD at the start of the narrative.
2025 + 6 months = 6.2025.
Additionally, there's a multi-part prologue that includes another title card at the start of the longest part letting us know we're in "ALASKA - 2020 KAIJU WAR YEAR 7". That means the long middle part presumably takes place in 2020 AD and the first parts depicting the first kaiju attacks must therefore take place in 2013 AD.
2020 - 7 = 2013.
Finally, as part of the science-fiction technology that allows for the coordinated double-piloting of giant robots, characters consistently see bits of memories of their co-pilots. These flashes are unplaceable other than taking place during the natural human lifespans of the characters' pasts pre-2020 AD, i.e. the late 20th century and early 21st century.