When Does "Them!" (1954) Take Place?
"Them!" is a science fiction horror film written by George Worthing Yates with Ted Sherdeman and Russell Hughes that released June 18th, 1954. So when is "Them!" set?
It takes place in the year:
We know this because later in the story a Los Angeles movie theater can be seen and its marquee reads "3 Sailors and a Girl" and the film "Three Sailors and a Girl" (1953) released on November 23rd, 1953 AD. So it must be during or after November of 1953 AD by that point.

1954 AD
We know this because later in the story a Los Angeles movie theater can be seen and its marquee reads "3 Sailors and a Girl" and the film "Three Sailors and a Girl" (1953) released on November 23rd, 1953 AD. So it must be during or after November of 1953 AD by that point.
More specifically, about one-third into the tale Doctor Harold Medford says, "1945. That's 9 years ago."
1,945 + 9 = 1,954.
Specifically, Dr. Medford's arrival is announced by an advance telegram dated for "SEP 9" representing September 9th. So it's September of 1954 AD at this point and almost certainly mid 1954 AD at the beginning.
Later, General Robert O'Brien's broadcast about martial law claims, "A couple of months ago in the desert of New Mexico, gigantic ants were discovered.", a scene audiences saw not long after the September telegram is delivered. Since the phrase "couple of months" usually means 2 or 3 months, it's certainly either November of 1954 AD or December of 1954 AD by the end.

