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Godzilla is a fictional giant monster originating from a series of tokusatsu films of the same name from Japan. It first appeared in Ishirō Honda's 1954 film Godzilla
Aliases: : King of the Monsters; Gigantis; Monster Zero-One; God of Destruction; Alpha Predator;
The Wikipedia page states this about his origins:
Although his origins vary somewhat from film to film, he is always described as a prehistoriccreature, who first appeared and attacked Japan at the beginning of the Atomic Age. In particular, mutation due to atomic radiation is presented as an explanation for his size and powers.
It also states that the design of Godzilla has been largely inspired by a number of dinosaurs, although the ones listed there span the Late Jurassic through Late Cretaceous periods, some 50 million years or more after the Triassic period:
Godzilla's approximate appearance, regardless of the design of the suit utilized for the creature, remains the same general shape, which is instantly recognizable: a giant, mutant dinosaur with rough, bumpy charcoal-grey scales, a long powerful tail, and jagged, bone-colored dorsal fins. Godzilla's iconic character design is a blended chimera inspired by various prehistoric reptiles, gleaned from children's dinosaur books and illustrations from an issue of Life magazine: Godzilla has the head and lower body of a Tyrannosaurus, a triple row of dorsal plates reminiscent of a Stegosaurus, the neck and forearms of Iguanodon and the tail and skin texture of a crocodile.1,2
William M. Tsutsui (2003). Godzilla on My Mind: Fifty Years of the King of Monsters. New York: Palgrave Macmillan. p. 23.
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In-universe, the movie Godzilla vs. King Ghidorah (1991) shows that Godzilla mutated from a Godzillasaurus, a species of therapod which had survived on Lagos island until World War II. An incident with a nuclear submarine irradiated it, creating Godzilla.
Based on the above, Godzilla would be more related to prehistoric dinosaurs than lizards of today.