No, the 1954 Godzilla movie was one of Godzilla's earliest works, but it was not the earliest. The name Godzilla first appeared in a Japanese manga of the same name in 1942. Before that, there were other forms of Godzilla's image, such as appearing in news reports, posters, and advertisements.
Godzilla was a famous Japanese monster that appeared in many movies and games. The following are the names of the movies where Godzilla fights other versions of monsters:
1 Godzilla: King of Monsters (2004) -Godzilla's debut movie was produced and distributed in Japan.
Godzilla 2: Monster Island (2014) -This movie is a continuation of Godzilla, produced and distributed in Japan.
Godzilla: Monster Planet (2017) -This movie is a derivative work of Godzilla, produced and distributed in Canada.
Godzilla: Rise of Darkness (2020) -This movie is a remake of Godzilla, produced and distributed in Japan and Canada.
Godzilla: Rise with the Sun (2019) -This film is Godzilla's international collaboration, produced and distributed in many countries.
Godzilla: Wolverine (2020) -This movie is a superhero movie about the battle between Godzilla and Wolverine.
Godzilla: Spirited Away (2010) -This movie is an animated film by Godzilla, produced and distributed in Japan.
8 Godzilla: Monsters Power Corporation (2015) -This movie is an animated film by Godzilla, produced and distributed in Japan and Canada.
Godzilla: The Big Movie 2 (2018) -This is the second film in a series that was produced and distributed in Japan.
Godzilla: Monster House (2005) -This movie tells the story of Godzilla in a house. It was produced and distributed in Japan.
Hard to say. You'd need to look into the background and the creator's intentions. Sometimes stories are inspired by real-life but have fictional elements added. Without more information, it's tough to determine if Aaron Wallace is truly a true story.
Godzilla Earth is not a fanfic. It has its own official production and creative process, distinct from fan-created works. It's a legitimate entry in the Godzilla canon.