Godzilla's movements and mannerisms namely the scene where he's sleeping curled up inside the Roman Colosseum, were based off of director Adam Wingard's cat 'Mischief.'
The image used for the blueprint of the B.E.A.S.T. Glove is the arm of the Pacific Rim (2013) jaeger, Gipsy Danger.
Godzilla has 8 minutes of screen-time, which as actually the least amount in the Monsterverse movie at the time of release. For comparison this is 3 minutes less than Godzilla vs. Kong (2021) (which was 11 minutes), and 2 minutes less than Godzilla: King of the Monsters (2019) (which was 10 minutes) and Godzilla (2014) (which was 10 minutes).
With a net budget of $135 million, this is the cheapest MonsterVerse film to date.
Godzilla's new design here has purple/pink-colored plates akin to the MireGoji design from Godzilla 2000 (1999) and Godzilla vs. Megaguirus (2000) and a pink atomic breath akin to the violet one from Shin Godzilla (2016). Creature designer Jared Krichevsky also cited the plates from the Godzilla Ultima design from Godzilla Singular Point (2021) as direct inspiration.