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Given the nature of the Godzilla franchise, it's highly unlikely that we'll be getting much more violent than "I hit you in the face!"
Most of Godzilla's movies have never gone into extreme gore, with only three notable exceptions. Godzilla vs. Mechagodzilla (1973) where there was a lot of blood. Godzilla vs. Mechagodzilla II (1992) where there was blood and Godzilla's secondary brain was destroyed. And GMK, where Godzilla bled profusely once the missile had detonated in his neck, and then his body was destroyed leaving only a beating heart at the bottom of the sea.
However, again, the likelihood of "violence and gore" is very slim. The Godzilla franchise has never been about creature violence so much as "monster vs. monster fun." The most gore we're likely to see is one monster hitting another, and that's about it.