I would make a strategy game where you play the Kaiju Response Force tasked with protecting the world from kaiju.

Starting out with basic modern military equipment, you'd be sent in in somewhat X-COMish gameplay where your forces are pitted against gigantic kaiju, swarms of little minions and sometimes aliens directing the monsters, with the goal of keeping civilians safe while finding some way to stop the titanic terrors.

The gimmick of the game would be that every kaiju would be procedurally generated, with a unique name, basic powerset, appearance based on hundreds of potential subspecies, and goals (make a nest, find a mate, FUCK SHIT UP, anything a kaiju may want.)

You wouldn't be killing a kaiju in a single sortie, every one would be persistent and have a presence on the world map where they'd emerge and you'd have to keep track of them and find means to hurt them, whittling them down over time. The ways to do this would be extremely varied and up to player choice:
>Develop missiles that can bore through their skin
>Research weak spots unique to each monster you can target during missions
>Reverse-engineer alien tech to mind-control the kaiju and make them obey your commands (and risk them breaking free at an inopportune moment in the future)
>Make contracts with peaceful kaiju to gain their assistance
>Find deceased kaiju and construct mechs from their bones
The list goes on and on. You could even just wait for kaiju to meet one another and sit back to watch them duke it out.

Total freedom in kaiju-fighting fun would be my goal. Win or lose, have fun stepping in the shoes of those poor motherfuckers that in every kaiju film get sent to duke it out with beasts a thousand times their size. Ideally, you could get free DLC to import actual kaiju like Godzilla and Toho's monsters, Gamera, Pacific Rim kaiju, the Beast From 20,000 Fathoms, King Kong, and so on.

https://www.youtube.com/watch?v=_8IQFyoxCxs