When Does the TV Show "Legends of Tomorrow" Season One 1st Part (2016) Take Place?

"Legends of Tomorrow" season one is a comedy science fiction television series showran by Phil Klemmer with Chris Fedak [adapting "Showcase" #20 (1959) by Dave Wood, "Time Masters" #1-#8 (1989-1990) by Bob Wayne with Lewis Shiner as well as the Hawkman story in "Flash Comics" #1 (1939) by Gardner Fox] that first released January 21st, 2016. So when is "Legends of Tomorrow" season 1 episodes 1 to 7 set? 

It takes place on an alternate timeline of the fictional DC Films Universe in the year: 

The End of Time 

We know this because in season 1 episodes 1 "Pilot, Part 1" and 2 "Pilot, Part 2", soon after the prologue, Rip Hunter is asking Gideon, his time-traveling ship's on-board artificial intelligence to "Set a course. United States. Star City. January, 2016." and in season 1 episode 4 "White Knights", Rip says to his team, ..."your former lives in January 2016." The first episode's early portion then includes a superimposed title card announcing visiting "TIBET  2016", "PITTSBURGH  2016", "ST. ROCH  2016", and "CENTRAL CITY  2016". There's three flashbacks in season 1 episode 14 "River of Time" to show moments from the final day before some of the characters leave their "former lives". So we know it's January of 2016 AD at the start of the season. 

More specifically, many important scenes take place in the Time Masters Council, which is in "The Vanishing Point" where Chronos tells us, "time doesn't exist there the way it does on Earth." These scenes are often labeled with the title card "TIME MASTERS COUNCIL". Season 1 episode 7 "Marooned" contains flashbacks to Rip's past in "The Vanishing Point", and season 1 episode 12 "Last Refuge" begins in this setting for a first of two prologues. The Vanishing Point is clearly analogous to other fictional portrayals of The End of Time. The season's final series of episodes ("River of Time", "Destiny", and "Legendary") take place in this setting. 

Additionally, there's a 2166 AD prologue and the very first shot of the very first scene of season 1 episode 1 "Pilot, Part 1" includes a title card reading "LONDON  2166". Season 1 episode 13 "Leviathan" brings the "Legends" to the year 2166 AD with another "LONDON  2166" title card and a real confirmation of the year with Rip's line: "Here in 2166, they've subjugated most of the globe." 

Before "Part 1" is even halfway over, the characters arrive on their first adventure in time. Professor? Ray Palmer says, "This is unbelievable. 1975." and very soon a calendar can be seen in the background with "1975 ACADEMIC YEAR" at the top. The episode's conclusion and the beginning of "Part 2" is in "NORWAY  1975". Rip Hunter even specifies it is "October 19th, 1975" so it's certainly October of 1975 AD. 

Season 1 episode 3 "Blood Ties" begins with a short prologue that opens immediately with an "ANCIENT EGYPT  1700 BC" title card and there's a flashback later that picks up where this prologue leaves off. Though most of the episode continues the 1970s setting with "LEIPZIG  1975" and "CENTRAL CITY  1975", at least these two parts probably take place in 1700 BC. There's also a prologue taking place in this same setting at the start of season 1 episode 14 "River of Time" and Vandal Savage directly refers to this era when he says, "4,000 years ago, it was you who was the prisoner." in a scene set in 2166 AD. This would make these scenes in 1834 BC. 

2166 - 4000 = -1834. 

Season 1 episode 4 "White Knights" the characters visit the twentieth century again and it's clear because the US Department of Defense fax Gideon finds in archives leading the team to this moment includes the date "January 26, 1986". Plus, Rip almost immediately says to the crew, "The year is 1986." and there's a multitude of references across episodes 3, 4, and 5 to the then-ongoing Cold War between the United States of America and the Soviet Union, which lasted from 1947 AD to 1991 AD. Furthermore, a title card at the very first shot of the episode reads "WASHINGTON, D.C.  1986" so it's sometime after January and certainly within the 1986 AD calendar year. 

Season 1 episode 6 "Star City 2046" debuts the setting of the 2046 AD futuristic setting of the city featured in some episodes of "Arrow". Posters are visible in the background telling citizens to "VOTE McCallister" ... "FOR PRESIDENT IN 2040" so it must be after November of 2040 AD. The time is more clearly identified when Rip says, "This... this is 2046." quite early after their arrival and by a superimposed title card reading "STAR CITY  2046" soon afterward.