I can only imagine a Godzilla anime being done like Digimon or Pokémon (or Gundam Build Fighters, I hope) style, with Godzilla and co. being partnered with a kid.
The story could tell that the result of big kaiju war, where Mothra, in a desperate moment, sealed all kaijus (herself included), in order to save humanity.
Cue years later when talismans that contain the kaijus are discovered by archeologist (from the far future), only to be attacked by the terrorist organization Red Bamboo, who want the talismans for themselves, but one of the archeologist escape with one of the Talismans (Godzilla). He gaves it to his son before being killed by the red bamboo, and now the child and godzilla will have to find the other talismans and stop the evil Red Bamboo.
"There are 4 things that I've learned to dont discuss, because they end with people killing each other: Religion, politics, sports, and logic on anime and kaiju movies"