When Does the Film "Mothra" (1961) Take Place?
"Mosura" is an adventure horror (kaiju) film written by Shinichi Sekizawa [adapting "Hakkō Yōsei to Mosura" (1961) by Takehiko Fukunaga, Shinichiro Nakamura, and Yoshie Hotta] that released July 30th, 1961. So when is "Mothra" set?
It takes place roughly in the years:
We know this because the destruction of the unique real-world Kurobe Dam is shown. Water is shown breaking through and (though the dam was not completed until 1963 AD) the reservoir began to be filled with water in October of 1960 AD. A Mobil gas station can be seen being destroyed by Mothra three-quarters through the story with the red Pegasus logo introduced in 1911 AD prominently visible, this logo was officially replaced on February 7th, 1966 AD though some locations probably continued to use it. A Pan-American Airways plane is also seen on-screen and Pan-Am went out of business on December 4th, 1991 AD. So it must be after late 1960 AD and before late 1991 AD; most likely before early 1966 AD.

1960s AD
We know this because the destruction of the unique real-world Kurobe Dam is shown. Water is shown breaking through and (though the dam was not completed until 1963 AD) the reservoir began to be filled with water in October of 1960 AD. A Mobil gas station can be seen being destroyed by Mothra three-quarters through the story with the red Pegasus logo introduced in 1911 AD prominently visible, this logo was officially replaced on February 7th, 1966 AD though some locations probably continued to use it. A Pan-American Airways plane is also seen on-screen and Pan-Am went out of business on December 4th, 1991 AD. So it must be after late 1960 AD and before late 1991 AD; most likely before early 1966 AD.
Furthermore, Doctor Shinichi "Chujo" Tyuujou holds a file on wealthy Rolisican (a composite of Russia and the United States of America that only exists in the movie's fictional world [diegesis]) industrialist Clark J. Nelson that reads "April, 1954, he went on an expedition at upper stream of Ama-zon" then, lower, "His expedition to Upper Amazon-River in 1954, finished in failure." and, immediately after reading it, Dr. Chujo says, "In 1954, he made an expedition to the Amazon". This sets us absolutely after 1954 AD, HOWEVER, the dialogue in this place in the American cut reveals something further. See below.

It has been retroactively absorbed into the MonsterVerse Universe at a chronologically early spot (a first chronological film to feature Mothra) and can be watched at its timeline point with or without the "Monarch: Legacy of Monsters" (2023) TV show.
An Americanized cut written by Robert Myerson (released to American audiences as "Mothra") was made for American audiences and released May 10th, 1962.
It takes place roughly in the years:
early 1960s AD
In this version, Dr. Chujo says, "Several years ago, he went to the Amazon" after reading the file including the April of 1954 AD date for Nelson's upper Amazon River expedition. Though this is vague it's unlikely the character would have chosen the word "several" if it has been more than a decade since April of 1954 AD, putting us somewhere after late 1960 AD (because of the appearance of the real-world Kurobe Dam) but probably before 1964 AD.
It has been retroactively absorbed into the MonsterVerse at a chronologically early spot (a first chronological film to feature Mothra) and can be watched at its timeline point.