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

"Legends of Tomorrow" season one episodes one to ten 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 premiered January 21st, 2016. So when is "Legends of Tomorrow" season 1 episodes 1 to 10 set? 

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

2016 AD/1975 AD 

We know this because before "Part 1" is even halfway over the characters arrive on their first adventure in time. Doctor 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. The first half of the season's longest stretch in one setting over any series of episodes ("Pilot" Parts 1 & 2, and "Blood Ties") takes place in this setting. 

Also, 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. 

Additionally, 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". The Vanishing Point is clearly analogous to other fictional portrayals of The End of Time. 

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" back 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." 

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 short parts 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 in season 1 episode 16 "Legendary" when he says, ..."erase time itself and travel us back to 1700 BC." 

For season 1 episode 4 "White Knights" and season 1 episode 5 "Fail-Safe" 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 for these two episodes. 

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. 

Season 1 episode 7 "Marooned" takes place entirely outside of time. 

Finally, season 1 episode 8 "Night of the Hawk" and season 1 episode 9 "Left Behind" bring the group to the 1950s and it's nailed down when the A.I Gilbert declares at the end of the previous episode, he has determined they should go to "Harmony Falls, Oregon in March of 1958" next. When Jefferson "Jax" Jackson says, "I thought girls from 1958 moved a little bit slower!" halfway through episode 8 we get a fun confirmation that they took Gilbert's advice. Plus, the very first shot of episode 8 includes the title card: "HARMONY FALLS  1958". So it's certainly March of 1958 AD. The character return to this setting in season 1 episode 16 "Legendary". 

Then, season 1 episode 9 "Left Behind" even moves forward from there. Ray and Kendra Saunders/Hawkgirl posed as a married couple and he says, "Happy second anniversary." making 2 full years since the beginning of episode 8 meaning it's March of 1960 AD. A superimposed title card also reads "TWO YEARS LATER" and the ship's onboard A.I Gideon says to Rip, "then again, this is 1960." 

3.1958 + 2 = 3.1960. 

Finally, season 1 episode 10 "Progeny" Rip's motley crew arrives in 2147 AD. Just at the very end of episode 9 "Left Behind", Rip demands, "Gideon, plot a course for Kasnia Conglomerate, the year 2147." Furthermore, early in episode 10, a title card labels it: "KASNIA CONGLOMERATE  2147". During episode 13 the Gideon A.I. replays a moment from the end of episode 10 after Leonard Snart/Captain Cold says, "Gideon, show her the footage: Kasnia, November 3rd, 2147." so it's November of 2147 AD. 

This episode also features three flashbacks: the first of which begins with a shot of a standing calendar with "1920 OCTOBER 1920" at the top. The second one includes close-ups of documents dated for "the 21st day of January in the year 1920" but is implied to take place after the first. So it's certainly October of 1920 AD at this point. 

It is a TV series in the DC Films multiverse timeline but takes place outside of time or all along the timeline and, therefore, can be watched any time after "The Flash" season two (2015) and "Arrow" season four (2015).