I searched this up and it just shows up a wikipedia about the Aztec Empire Army, I read it and I read the last part of the Aztec Empire Army wikipedia and it doesn't show up a single thing about them having a navy. (What I fully meant was did they create wooden boats in there time or not, but you can ask me if they do have a navy or not as well).
Yes they did create timber vessels however they were not used for seafaring and served to travel in freshwater. Either by rivers for trade or on still water for example in the capital city of Tenochtitlan*, now modern day Mexico City, for navigating the city centered in a large lake.
TLDR; No navy as such as they didn't take to the sea. But did have small timber vessels.
*EDIT: It is perhaps misleading to call the city of Tenochtitlan a 'capital' city. As the Aztec Empire was a hegemonic empire, it is perhaps more useful to think of Tenochtitlan as sitting at the head of the empire, exerting control over, and taking tribute from subjugated city-states and tribes.