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.
Godzilla might see the pregnant Muto as a threat. After all, Mutos are his enemies. So he could start hunting it down to prevent more Mutos from being born.
Naruto would probably be both amazed and a bit scared at first. But being Naruto, he would quickly jump into action. He might try to use his rasengan against Godzilla, thinking it could do some damage. However, he would soon realize that Godzilla is much more powerful than he initially thought and would have to come up with a different strategy, like using his speed to avoid Godzilla's attacks and find its weak points.
Shinji would probably be terrified at first. He's already hesitant and scared in his normal battles, and Godzilla is much larger and more intimidating than the Angels he usually faces. Asuka would likely be more aggressive, thinking she can take on Godzilla with her Eva. Rei, on the other hand, would be very calm and observant, trying to understand Godzilla's nature. Misato would be in a panic initially, but then quickly start strategizing on how to deal with this new threat. Gendo would see Godzilla as either a new opportunity or a major obstacle depending on his long - term plans.
Some of them might be amused. For instance, Hulk could find it funny if Godzilla was shown as being weak in the fanfiction. He might laugh and say 'That big lizard not so tough!'.
Some of them would be amused. Hawkeye might chuckle at the outlandish scenarios in the fanfic. Black Widow would be more reserved but still interested. She'd be quietly observing and thinking about the implications of the story. Captain America would try to find the moral of the story, if there is one, as he always does.
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.