Like cloche hats, pet rocks, flip phones, and slap bracelets, Godzilla is definitely a product of its time. Lucky for the King of the Monsters, his movie aged better than those other fads. Except for cloche hats: those are still stylish as all get out and are welcome to make a comeback.
Godzilla was released in 1954, and this is key to understanding how Godzilla became, well, Godzilla. That year was just shy of a decade after the atomic bombs were dropped on Hiroshima and Nagasaki and the end of World War II, and two years after the end of the American occupation and reconstruction of Japan. To show the importance of this time to the movie's themes and characters, its story is set in the same year—or, at least, a close enough equivalent.
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As David Kalat noted in his commentary for the Criterion release of Godzilla, the unique era it was developed meant that the story folded in lots of the concerns in Japan at that time.
For example, mere months before Godzilla's release, the Daigo Fukuryu-Maru incident rocked Japan. The Daigo Fukuryu-Maru was a fishing boat that sailed too close to an H-bomb blast from a United States test on the Marshall Islands. The crew was irradiated and grew sick, and one of them, Aikichi Kuboyama, died on September 23, 1954. He was the latest of the Japanese victims of nuclear weapons.
Godzilla used this incident as inspiration for its opening scenes, where the titular beast attacks Japanese ships and kills their crews. These opening scenes jump headfirst into the film's anti-nuclear message, and the film doubles down later when it includes imagery that harkens back to the bombings of Hiroshima and Nagasaki, such as the landscape of Tokyo being devastated by Godzilla's atomic breath and the field hospital staff checking victims for radiation sickness.
The Daigo Fukuryu-Maru incident spurred the nation's anti-nuclear sentiments and protests, but other groups argued restraint to keep the nation's foreign relationships strong. Kalat further notes that this timely debate was incorporated into the film during the Diet committee argument. You may remember the scene; it went a little something like this:
OYAMA: Quiet! What I mean is if this Godzilla thing is the result of H-bomb tests—
WOMAN: It is! That's exactly what it is!
OYAMA: That's my point. Make this public, and our fragile diplomatic relations will be further strained.
WOMAN: The truth is the truth!
OYAMA: That's what makes it so serious! If we announce this too rashly, the public will panic. Our political life, economy, and foreign relations will be plunged into chaos!
WOMAN: You fool! What are you saying?
The fact that THIS debate could even be included in the film is also important to its setting. Two years earlier, during the occupation, the Japanese weren't allowed to protest or criticize the United States' usage of nuclear weapons, either the bombings of Hiroshima and Nagasaki or the continued testing in the Pacific.
As film historian Tadao Sato points out:
The occupation forces emphasized freedom of speech, yet they didn't allow criticism of the occupation forces themselves. So they enforced strict censorship while claiming to do the opposite. So it wasn't official censorship. The occupation forces were most concerned about censoring anything about the atomic bombs (Source).
As a result, this scene shows the Japanese nation lifting the gag order and reasserting its self-reliance. Sure, they haven't figured out all the answers; what nation has? But during the occupation, the Japanese wouldn't have been able to have these conversations, protest perceived injustices, or make these decisions.
In a bit of meta-commentary, the movie Godzilla joined the nation's conversation by presenting its anti-nuclear weapon message as an allegory wrapped in a monster movie. Apparently, Godzilla isn't only the destroyer of buildings, but also fourth-walls.
Finally, we should consider the importance of the military to the setting. During
World War II, the Japanese military conquered many countries, such as China and Korea, and invaded several more. The goal was to create an empire in the vein of Western colonial powers. To make a long story short, they upset the United States by attacking Pearl Harbor, and the U.S. accepted the country's surrender on September 2, 1945.
Flash forward to 1954, and we see the establishment of a new kind of military for Japan, the Japan Self-Defense Forces. As the name implies, the armed force is not used as an invading military but only for defense of the country from invasion. Oh, and they sometimes deploy as part of UN peacekeeping operations, but that's a whole other thing.
Godzilla highlights this new role of the Japanese military and recasts them as heroic in the face of Godzilla. Although their weapons are useless against the fire-breathing beast, they do all they can to protect the population of Japan. They use depth charges to try and take care of Godzilla before it comes ashore. They set up an electric fence. And during the attack on Tokyo, they defend the city against Godzilla despite their weapons being useless against it.
In all these cases, the Japanese are able to take pride in the representation of their armed service members, which had been difficult to do after a period of aggressive expansion and a massive military defeat. It's another example of Godzilla incorporating then-current events to discuss Japan's new path during the second-half of the 20th century.