In this alternate history, Christopher Columbus makes landfall in Central America, after passing south of Florida and sailing through the Gulf of Mexico, arriving right on the doorstep of the Aztec Empire.
The First Contact goes badly and most of the expedition is slaughtered. The survivors are taken prisoner and the Aztecs salvage everything they can from Columbus' ships.
Could the Aztecs do something useful with this new technological knowledge; applying and reusing it for their gain, becoming the major power of the Americas and ending up sending their own expedition back to Spain?
In this alternate history, with no news of Columbus, Europe assumes that he is lost and nobody sends another expedition, deeming the very idea foolish. The European powers focus on Africa and Asia.
EDIT: To address some points:
I'm only dealing with Columbus first arrival. What happened after that in our history won't happen in this alternate version. Please don't answer with examples of later Conquistadors who came armed to the teeth or what happened when the conquest was in full swing.
This is part of the background of the alternate history that I want to make as believable and coherent with what we know of this time as possible, technology-wise. I'm not going to write the story of this alternate First Contact.
I'm well aware that what defeated the original civilizations of the Americas are the diseases brought by the Europeans, more than weapons or anything else. That's another fact that I'll deal with later.
The expedition that the Aztecs would send back to Spain isn't sent to conquer Spain and Europe, but merely to establish formal contact with the people from the other side of the ocean.