I would argue no, but it depends on what you mean by "mythology". Still, the Persian Šah Namah alone probably eclipses the bulk of primary sources on Greek Mythology - it is by some reckonings 50% longer than the Odyssey and Iliad combined. Indian epic like the Mahabharata cycle is similarly extensive.

What is moreover comparatively speaking notably lacking in preserved Ancient Greek records are hymns of the kind found in the Vedas and the Avesta, which give us an entirely different perspective on myth-as-religion by providing us with a glimpse of the actual practice of the religion rather than the storytelling epic, legends and stories one might think of at first.

Furthermore, "Greek mythology" was far from a singular thing and the way we think if it as such owes a lot to popular cultures and modern attempts to harmonize divergences in the scattered handful of really good sources we have (Homer, Hesiod and some much later works, basically).

In any case, I would argue that the way Classical Greece preserved written history (not just records but histories) was unusual or even unique for its time, but the way it preserved mythology... not so much.