Which Final Fantasy game marked the first appearance of Moogles?

The first appearance of Moogles was in Final Fantasy III.

In the 1990 game, Moogles appear as cave-dwelling creatures who guard the mage Doga. They were created by artist and game designer Koichi Ishii, whose early concept was inspired partly by an all-white koala with wings.

Moogles were planned for Final Fantasy II under the name “Cryon,” but that creature was ultimately reworked into the Giant Beaver. They were then incorporated into Final Fantasy III, making it the correct answer rather than Final Fantasy IV or V.

Later games greatly expanded their role. Moogles became messengers, shopkeepers, save-point helpers, summoned creatures, housekeepers in Final Fantasy XI, and major characters such as Mog. Their designs also changed over time, especially after later artists added or refined features such as the pom-pom antenna and wings.