Turquoise is usually found in conjunction with copper ore. If there are copper deposits in Mexico or Central America it would not be surprising to find turquoise there.
The question is where are they? If any of note.
There probably are copper deposits in Mexico.
The Aztecs had quite a few copper axes, as documented in the Discovery and Conquest of Mexico.
There are large copper deposits in that area. The ancient groups made their ceremonial knives and parts of their masks from copper.
My thought is also that when the meteor hit 65 million years ago a large amount of copper ore and minerals would have been blasted out and traveled into large areas of North and South America.
This doesn’t count the other copper ore deposits that were not touched by the massive blast.
This is how the Iridium layers from the meteor itself was spread in layers of sediment throughout the world.