When Does "The Matrix" (1999) Take Place?
"The Matrix" is a science fiction film written by Lana Wachowski with Lilly Wachowski and released March 31st, 1999.
We know this because midway through the movie Morpheus says to Neo, “You believe it's the year 1999, when in fact: it's closer to 2199. I can’t tell you exactly what year it is because we honestly don’t know.” In the sequel to this film, “The Matrix Reloaded” (2003), the program named The Architect shockingly reveals that, in fact, "The Matrix is older than you know" and "this is the 6th version" meaning there has been, at least, 6 loops of roughly 100 years each since the first creation of the Matrix and not the 100 years Morpheus believed it has been.
It takes place on the fictional The Matrix timeline roughly in the year:
~2699 AD
We know this because midway through the movie Morpheus says to Neo, “You believe it's the year 1999, when in fact: it's closer to 2199. I can’t tell you exactly what year it is because we honestly don’t know.” In the sequel to this film, “The Matrix Reloaded” (2003), the program named The Architect shockingly reveals that, in fact, "The Matrix is older than you know" and "this is the 6th version" meaning there has been, at least, 6 loops of roughly 100 years each since the first creation of the Matrix and not the 100 years Morpheus believed it has been.
100 x 5 = 500
and
2199 + 500 = 2699.
The timeline of the Matrix Universe is fairly unique among the largest franchises because the human characters within its fictional world (diegesis) do not themselves know what year it truly is for the duration of most of the stories.
Morpheus' hovercraft, the Nebuchadnezzar, has a plaque on-board which reads, "MADE IN THE USA YEAR 2069 A.D." We must presume this was either made by people freed from the Matrix who guessed at the correct date in "the real world" outside the Matrix or the ship is actually, over 500 years old, has been continuously repaired, and the humans are unaware of this.
The very beginning depicts a screen showing a phone call tracing program. As this program boots up, a string of numbers is visible at the top that reads “Call trans opt: received. 2-19-98 13:24:18 REC:Log>”. Presumably, this timestamp means the very next scene takes place at around the same time on the current calendar within the Matrix: February of 1998 AD.
Early in the story, Neo is introduced while asleep at his computer. A program is searching for current information about Morpheus and an article in Arabic is visible on his screen. It discusses religious unrest in Syria during the late 1990s.
At the end, we see a screen with the same phone call tracing program running. As the program boots up this time, it reads, “Call trans opt: received. 9-18-99 14:32:21 REC:Log>” meaning September of 1999 AD. The scene that follows seems to take place on this date on the current calendar within the Matrix.
These timestamps clearly refer only to time for the characters living within the Matrix who accept the false narrative they are presented: that it is still the late 20th century. In the video game "The Matrix Online" (2005), Tic Tock explains that the calendars and clocks within the Matrix are (or maybe previous to the events of “The Matrix Revolutions” (2003) were) periodically reset.
It is the first chronological film in The Matrix Universe timeline and can be watched at its timeline point or entirely separately.
It was adapted as part of a video game "The Matrix: Path of Neo" in 2005.
This SceenRant article explains timeline of The Matrix universe.