When Does the Musical "Anastasia" (2016) Take Place?
"Anastasia" is a historical fiction stage-musical written by Terrence McNally with Stephen Flaherty and Lynn Ahrens [adapting "Anastasia" (1952) by Marcelle Maurette] first performed May 12th, 2016. So when is "Anastasia" set?
It takes place in the year:
We know this because during the eighteenth song, "Crossing a Bridge", Anya (loosely based on the real-world Grand Duchess Anastasia Nikolaevna) and Dimitri meet on the real-world Alexandre III bridge in Paris, which was completed in 1900 AD. So it must be after 1900 AD. Act 1 begins with Deputy Commissioner Gleb Vaganov announcing that the city of St. Petersburg has been renamed Leningrad ("The Tsar’s St. Petersburg is now the people’s Leningrad!"), which happened in the real world on January 26th, 1924 AD. So it must be during or after 1924 AD at this point.

1927 AD
We know this because during the eighteenth song, "Crossing a Bridge", Anya (loosely based on the real-world Grand Duchess Anastasia Nikolaevna) and Dimitri meet on the real-world Alexandre III bridge in Paris, which was completed in 1900 AD. So it must be after 1900 AD. Act 1 begins with Deputy Commissioner Gleb Vaganov announcing that the city of St. Petersburg has been renamed Leningrad ("The Tsar’s St. Petersburg is now the people’s Leningrad!"), which happened in the real world on January 26th, 1924 AD. So it must be during or after 1924 AD at this point.
Furthermore, during the seventeenth song, "Paris Holds the Key (To Your Heart)", the characters sing "Have you seen Josephine Baker shake it up?" The real-world dancer Josephine Baker first arrived in Paris in 1925 AD and became famous in 1926 AD. So it must be during or after 1925 AD.
More specifically, at the same time, a huge sign can be seen in the background of the stage reading "Paris 1927".
Additionally, there's the 1907 AD prologue seen during "Prologue: Once Upon a December", the musical's first song, in which Anya is considerably younger than she is during the main action.
Immediately afterward, the audience gets a flash of the violence of the Russian Revolution, dramatically depicted in the second song, "The Last Dance of the Romanovs". The Russian Revolution happened in stages, starting in March of 2017 AD and then continuing in November of 2017 AD in the real world. Also, a huge projection onto the back of the stage at this time declares that it is "1917". So it is accurately 1917 AD.
Finally, the third quick prologue shows the real-world Dowager Empress Marie Feodorovna reading a letter and despairing out-loud, "All of them. All of them!?", implying she is receiving word of the execution of the Romanov royal family. In the real world, their famous and tragic execution occurred on July 17th, 1918 AD and the Dowager Empress first received word of it soon after, within the 1918 AD calendar year.