Had a lot of fun playing your game. I got Godzilla Singular Point and Attack of the Friday Monster vibes. As someone that loves kaiju and loves making kaiju games, I appeciate that you gave your kaiju and kyodi hero a sense of size.
For feedback I would say vary the obstacles more. You have rubble and destroyed buildings that could drop rocks or debris, same with the kaiju. Ramps would be cool too.
I think the music for the driving parts could be faster paced and have more of a racing feeling, the more somber and dramatic scores could be saved for the cut scenes.
In Godzilla 2000, there is a scene very close to the beginning, if not the very beginning, where the protagonists chase Godzilla in their car and then end up getting chased themselves. It might be a good source of inspiration for future updates.