When Does "Beren and Lúthien" (2017) Take Place?
"Beren and Lúthien" is a fantasy mixed novel/epic poem written by J.R.R. Tolkien with Christopher Tolkien* that released June 1st, 2017. So when is "Beren and Lúthien" set?
It takes place on the fictional Middle-Earth timeline in the years:
We know this because the beginning of the narrative is the first meeting of Beren and Lúthien and in "The Fellowship of the Ring" (1954) Aragorn son of Arathorn/Strider says, ..."the meeting of Beren son of Barahir and Luthien Tinúviel." and soon after "In those days the Great Enemy, of whom Sauron of Mordor was but a servant, dwelt in Angband in the North, and the Elves of the West coming back to Middle-earth made war upon him to regain the Silmarils which he had stolen; and the fathers of Men aided the Elves. But the Enemy was victorious and Barahir was slain, and Beren escaping through great peril came over the Mountains of Terror into the hidden Kingdom of Thingol in the forest of Neldoreth. There he beheld Luthien singing and dancing in a glade"...

FA 464 (I 464) - FA 496? (I 496?)
We know this because the beginning of the narrative is the first meeting of Beren and Lúthien and in "The Fellowship of the Ring" (1954) Aragorn son of Arathorn/Strider says, ..."the meeting of Beren son of Barahir and Luthien Tinúviel." and soon after "In those days the Great Enemy, of whom Sauron of Mordor was but a servant, dwelt in Angband in the North, and the Elves of the West coming back to Middle-earth made war upon him to regain the Silmarils which he had stolen; and the fathers of Men aided the Elves. But the Enemy was victorious and Barahir was slain, and Beren escaping through great peril came over the Mountains of Terror into the hidden Kingdom of Thingol in the forest of Neldoreth. There he beheld Luthien singing and dancing in a glade"...
Furthermore, in chapter 19 of "The Silmarillion" (1977) first "Beren buried his father’s bones" then "for four years more Beren wandered still upon Dorthonion" and then "In time of winter and snow" and then "wandering in the summer in the woods of Neldoreth he came upon Luthien", and this is the first scene of their story.
More specifically, in chapter 19 of "The Silmarillion" (1977) the moment that begins Beren and Lúthien's story is first described as being "in the summer" so it is certainly summer of FA 464 at the start.
As Aragorn tells the tale to the hobbits thousands of years later, "When winter passed, she came again / And her song released the sudden spring," so it must be spring of FA 465 by this point.
There are other calendars in this world as well but Shire Reckoning only starts at TA 1601 so there is no corresponding year in Shire Reckoning years. The in-universe anthropological study "Concerning Hobbits" that serves as the first part of the "PROLOGUE" to "The Fellowship of the Ring" (1954) specifically says, "About this time legend among the Hobbits first becomes history with a reckoning of years. For it was in the one thousand six hundred and first year of the Third Age that the Fallohide brothers... crossed the brown river Baranduin with a great following of Hobbits... Thus began the Shire-reckoning, for the year of the crossing of the Brandywine (as the Hobbits turned the name) became Year One of the Shire, and all later dates were reckoned from it."
At the end of his massive epic ("The Lord of the Rings", the Middle-Earth [the name of the continent] tales, the history of Arda [the name of the planet], Tolkien's legendarium– whatever name you please), the characters' trials are declared enough to mark the dawn of a new age: the Fourth Age, the Age of Man. On top of this, in "The History of Middle-Earth" (1983) story "Athrabeth Finrod ah Andreth" in volume 10 "Morgoth's Ring" (1993) it's stated by the omniscient narrator that Eru/Ilúvatar/the One "will himself enter into Arda, and heal Men and all the Marring from the beginning to the end." Lord of the Rings fans interpret this as a direct reference to the Jewish messiah concept and the "incarnation" of Eru/Ilúvatar/the One/The Christian God in the real-world spiritual leader Jesus Christ. Thus, the entire narrative can be seen as a mythological past of the Christian mythological narrative. There is the First Age (including the Years of the Lamps and the Years of the Trees). The First Age lasts 5,591 years ("ended with the Great Battle, in which the Host of Valinor... overthrew Morgoth"), then the Second Age lasts 3,441 years ("ended with the first overthrow of Sauron, servant of Morgoth"), the Third Age 3,021 ("came to its end in the War of the Ring") and, finally, the Fourth Age something in the neighborhood of 4,000 years. Essentially, this could be the period on the Gregorian calendar that we describe as "BC" (or "BCE") when the first Jewish mythological stories take place into the Fifth and/or Sixth Age. (And, incidentally, the period we mark as "AD" (or "CE") roughly after the birth of Jesus Christ, becomes the Sixth or Seventh Age.)
Using this logic, this calendar calculator places this story from 10336 BC to 10304 BC.
It is the earliest story in the Middle-Earth universe (except for the entire history of the universe as related in "The Silmarillion" [1977] and "The History of Middle-Earth" [1983]) and can be read before "The Children of Húrin" (2007).
*NOTE: Tolkien did not finish this story during his lifetime. Different parts were written in different ways and at different times and, as such, parts of the story are contradictory. A shorter but consistent version of this story can be found in "The Silmarillion" (1977) chapters 19, 22, and 24 plus a longer but inconsistent version in "The History of Middle-Earth" (1983) volume 2 "The Book of Lost Tales: Part Two" (1984), volume 3 "The Lays of Beleriand" (1985), and volume 4 "The Shaping of Middle-Earth" (1986).