Err.. What?

There were plenty of Nuclear tests in the Pacific during the 50's. I think those tests are what they are referring to, the ones on the Islands in the Pacific, notably the Marshall Islands.

The info is in the link: Pacific Proving Grounds: Nuclear Tests

Here are the details about the 1954 tests: Operation Castle -

'The Castle Bravo test of 1954 spread nuclear fallout across the Marshall Islands, parts of which were still inhabited.'

Main article: Operation Castle

'Six very large nuclear tests were conducted at the Bikini Atoll and the Enewetak Atoll as part of Operation Castle in 1954. The most notable was Castle Bravo, which was the first deployable (dry fuel) hydrogen bomb developed by the United States. Its yield, at 15 Mt was over twice as powerful as was predicted, and was the largest weapon ever detonated by the United States. It spread nuclear fallout over a wide area, including the Enewetak Atoll, Rongerik Atoll, Ailinginae Atoll, and Rongelap Atoll. An evacuation ensued, but many of the natives exposed suffered from cancers and a high incidence of birth defects. A Japanese fishing boat, the Daigo Fukuryu Maru, was additionally exposed and resulted in one death from radiation sickness, which gained considerable international attention.'

He brought this up in another thread. I still don't get why he thinks those two bombs are what was shown in the trailer when they say it's 1954. Castle Bravo was in 1954 and has generally been considered what awoke Godzilla. My original reply:

@M4inchan

Exactly where are you getting the idea that these were the 1945, tests? Operation Castle Bravo tested 6 dry fuel Hydrogen Bombs in 1954 in the Pacific Ocean. They're most likely referring to those tests.

Also the original movie does not state anywhere that fallout from an atomic bomb mutated Godzilla from Rongerik Island. The Godzillasaurus theory wasn't brought into the Godzilla series until 1991 when Godzilla vs. King Ghidorah was released. In the original film, Godzilla is not a Godzillasaurus mutated from the atomic bomb. He's simply some long dormant, perhaps evolved, aquatic/land animal that has survived and been awoken by the bomb.

He's right, if you know your history, you'll notice that nuclear tests were very common due to the Cold War. Tests of nuclear weapons were executed all throughout the 40's to 60's.

Godzilla wasn't mutated in the original film, only scarred by the bomb. Read anything about the creation of the film, they meant for him to look 'scarred and enraged' by the bomb-- even earlier designed showed his skin as being burnt and charred. 

^That's a design element I miss about Godzilla. His early Showa designs looked rough, inconsistant and chiseled. Heisei, Millennium and the 2014 versions don't really get that across very well anymore. Not so much a criticism as an observation.

The Trinity bomb test, the result of the Manhattan Project, took place in Alamogordo, New Mexico on July 16, 1945, NOT in the Pacific Ocean.  "Manhattan Project" refers to the general process of research and development of nuclear weapons, not to any actual nuke itself, and never really occured in any single place, let alone on an island.  Little Boy and Fat Man were the two bombs that were dropped on Hiroshima (August 6, 1945, NOT July 16) and Nagasaki (August 9, 1945, also NOT July 16) respectively.  Little Boy and Fat Man were neither "tests" (they were actual wartime bombings) nor done in the Pacific (unless you count Japan itself as "in" the Pacific).

As far as the year 1954 is concerned, that is most likely referring to the Operation Castle series of nuke tests, which DID take place in the Pacific Ocean.  The first of these tests was Castle Bravo in the Bikini Atoll, the largest nuclear bomb ever tested by the United States.

So I like...JUST NOW noticed that in the trailer, when Godzilla is rising out of the ocean next to the island....you can see IN THE SHOT the little bomb on it's wooden stand that was shown close-up in the shot before it. So Godzilla rising up actually triggered it (unless it was triggered remotely) and the white flash was the detonation. 

I'm sure I'm probably late to the party on this revelation, but eh, no harm, no foul. 

Before, I just thought it was a fade-out to white to show a separate shot of the same location being bombed in a separate scene, instead of it actually being one continuous shot, with the bomb included and everything.

Anyways, not directly on topic.

To answer your actual question: The FIRST nuclear tests were done in the 40's sure, but nowhere did they say that the FIRST tests were what awoke Godzilla. After that, nuclear testing continued, and was conducted on regular basis by several developed countries well into the 1990's. It's implied/assumed that it was these later tests which are relevant to the events in the film. 

As a side note, pretty much the only countries which do nuclear testing anymore are countries with relatively new nuclear programs, and even many of those are cold/sub-critical and/or underground tests. Basically nobody full-scale mushroom clouds islands/deserts anymore. 

When I locked at the trailer for he tenth time.... Ahem.... I thought about when he said that "we were trying to kill it wuh the nuclear tests." I thought that maybe he was talking about the MUTO. But Godzilla happened to be a side creation by accident. 

@Gigan3001, very unlikely, if you look at the bomb on the beach durn the Close-up shot, there is clearly a graphic representation of Godzilla painted on the side of the bomb with a circle and a line through it.  The bombs were used to try and kill Godzilla, it could be reversed and the MUTO's were created by accident, but they were definitely trying to kill Godzilla.