what new can they do with this tired concept?

They'll probably introduce time travel at some point

Introduce some musical elements.

My memory of the old Japanese Godzilla films is scant but wasn't there a movie where Godzilla was dancing what looked like the twist?

A kaiju ghost that is fucking up Tokyo and haunting Godzilla. It messes him up but he can't touch it back. Some cabal of mystics figure out how to open a window into the spirit world that mildly translates the physical into the ethereal/astral. They perform a massive ceremony that requires mass human sacrifice to open a large one that Goji can see. Then they fire a missile through it to give Goji the idea. So he lures the caustic giant kaiju spirit near it to try blazing it with his breath weapon through the huge window portal. The ghost is cagey and avoid destruction barely. Then stays away from the portal while wreaking even more havoc.
Our main human character is a magic neophyte and mountain climbing expert. He has been scaling Godzilla with his mt climbing gear and makes it out to Godzilla's hand. He sacrifices himself in a ritual to open a spirit window around Goji's hand. Godzilla sees the effect shrouding his hand and woops the fucking tar out of the ghost with that hand alone. Maybe even chokes the head of it right off.

There is no end to Godzilla ideas. Have you watched the old ones? Some cool stories (well ... cool plots. The human shit is always shit except maybe in King Ghidora)