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.
One idea could be to write a story from the perspective of a civilian caught in the middle of the Kaiju battles. Show their fear, their attempts to survive, and how they interact with the military trying to stop the Kaiju. Another could be a story about a Kaiju that has unique abilities not seen in the original lore, and how it changes the dynamic of the wars. Maybe it could be a Kaiju that can communicate with humans and tries to form an alliance against the more destructive Kaiju.
Some of the lesser - known Kaiju can also be interesting to include in fanfiction. For example, Rodan. He has his own unique abilities and personality. A fanfiction could explore his backstory more deeply, or create a new relationship between him and the other more well - known Kaiju. Anguirus is another one. He could be portrayed as a loyal ally to Godzilla, or have his own motives for being involved in the Kaiju Wars.
One popular character might be a kaiju girl with the ability to fly. Her aerial battles against other kaiju or threats are often a highlight in many fanfics. She is usually depicted as strong and independent.
A kaiju girls fanfic could also explore their origin stories. Maybe they were created by some scientific experiment gone wrong. The fanfic could delve into how they feel about their existence, whether they resent being different or embrace their kaiju side, and how they interact with the scientists who were involved in their creation.
I recommend Godzilla 2: King of Monsters to you. The plot is about aliens attacking and threatening Earth. At the same time, Godzilla fights with other giant monsters like Mosla, Ratton, and Kidora. In the end, Godzilla helps humans find little Godzilla and defeat the aliens with the other monsters. I hope you like this fairy's recommendation. Muah ~😗
For developing the plot, you could introduce a new, powerful enemy that neither Godzilla Earth nor the existing characters in the crossover world can defeat alone. So, they have to combine their strengths, like Godzilla Earth's raw power and the other characters' strategic thinking. As they fight together, they also face internal conflicts within their newfound alliance. Some may not trust Godzilla Earth completely, and this mistrust can create interesting sub - plots and character development. Eventually, through a series of events and battles, they overcome their differences and defeat the enemy. This could also lead to a changed world view for all the characters involved, and perhaps a new status quo for the fictional world.
One idea could be that Godzilla Earth teams up with a group of humans who have developed advanced technology to fight off an alien invasion. The humans initially fear Godzilla but soon realize they need his power.
Kaiju novels often portray kaiju as gigantic and powerful beings. They are usually depicted as forces of nature that are difficult to control or defeat. For example, in 'Godzilla' novels, Godzilla is shown as a nearly indestructible creature with its atomic breath and massive size.