Original Toho Films:
The 1954 film "Godzilla" (Gojira) established the origin of Godzilla as a creature mutated by nuclear testing. So the original origin is that he is a byproduct of nuclear radiation.
Monsterverse Films:
In the Monsterverse, the origin is changed. Films like "Godzilla" (2014) and "Godzilla: King of the Monsters" (2019), along with supplemental materials, establish that Godzilla is an ancient Titan.
These films depict Godzilla as a prehistoric creature that has existed for millions of years, acting as a natural force that maintains balance in the Earth's ecosystem.
Also the series "Monarch: Legacy of Monsters" further expands on the knowledge of Godzilla's ancient origins.
Therefore, while the original 1954 film shows a nuclear-induced origin, the Monsterverse films portray Godzilla as an ancient, natural entity.