One common theme is discovery. Just like in many 'baby kaiju fanfic', the baby kaiju is often exploring its new world, finding out about different places and things for the first time.
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.
Well, you could write a fanfic where a new type of kaiju is introduced into Kaiju Paradise. This kaiju has unique abilities that no one has seen before. The main character is a scientist or a researcher in the park who tries to study this new kaiju. Along the way, they face challenges from the park's management who don't want the public to know about this new discovery, and also from the kaiju itself which is very unpredictable.
One great 'baby kaiju fanfic' is 'The Little Kaiju's Adventure'. It follows a baby kaiju as it discovers the world around it, making friends with other small creatures. It's really cute.
To create engaging characters for Kaiju Paradise fanfic, think about their motives. Are they in the park because they are thrill - seekers or because they were forced to be there? Also, consider their relationships. A character could have a strained relationship with another character who blames them for a kaiju - related incident. And don't forget about their appearance. A character with a unique look, like a scar from a kaiju encounter, can be very memorable.