This is most interesting! and looking into these areas on cannon/guns, notably out of my range (pun intended) but fascinating to learn about.
What I found is that the De Sosa 'expedition' was anything but a sanctioned or official trek northward from Nuevo Leon in North Mexico to Pecos, near Santa Fe New Mexico.
He was actually a practitioner of a form of Judaism, and had been in trouble with officials in Nuevo Leon in 1589, so actually this was more of a diaspora to avoid further prosecution. His group was formed mostly of 'conversos' who perhaps were in similar denomination, whatever the case, this 'journey' would not have been equipped through official or military channels.
That being the case, I feel it unlikely he would have had access to the larger types of culverin, a term which seems to describe a scope of cannon in a range of sizes, all the way to what seems most like the 'deck or swivel/wall guns.
In this sense, the culverin, which is the ancestor of the arquebus (essentially hand held cannon), is indirectly (?) related to the small wall gun (esmeril) which the diminutive 'Gonzalez' "Come and Take It" cannon.
In this illustration of a culverin, relatively smaller in size to the larger carraige reminds me of the Gonzalez cannon. While small in size and manageable in weight, the idea was of course to provide a firing platform.
My thinking is that perhaps De Sosa, had these smaller versions of the culvern, mounted in makeshift carraiges in this manner. As smaller guns of less weight, they could have viably made the push up this challenging terrain with the carts. While larger artillery would obviously not be accessible to such an unofficial exodus, these smaller guns, much like weaponry in circulation among the population would be more easily obtained.
Illustrated, a smaller culverin mounted on carraige; the map of DeSosas journey into Nuevo Mexico; a demi-culvern, regarded as a 'medium' cannon ; the Gonzalez cannon as a comparative.
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