The convention among IT professionals is to pronounce it as "you en see". Just so you don't have to take my word for it, here are a couple examples of professionals using the term (one American, one British):
To answer your comment regarding the originator's intent: unlike the GIF format, which was invented by a single person, the UNC convention seems to have been hammered out jointly between a bunch of people at Microsoft and IBM, according to research someone already did on Unix Stack Exchange. This is a quote from a patent pertaining to the technology:
“the Universal Naming Convention was jointly invented by IBM and
Microsoft for use in their jointly developed Local Area Network (LAN)
(from patent US5341499, quoted here https://unix.stackexchange.com/questions/57428/official-description-unc-universal-naming-convention)
So group consensus was always the only standard for this abbreviation.
Regarding the Google search you quoted in your question: I don't believe the results can be trusted, because formally there is no such thing as "a UNC" or "an UNC". There is the naming convention ("the UNC"), and then there is a path name that follows the convention. The latter are usually called "UNC paths", "UNC names", etc., not just "UNCs" (although it's possible that some people might call them "UNCs" conversationally, as a personal shorthand). Doing a Google ngram search for "a UNC path" vs "an UNC path" shows "a UNC path" starting to rise in use around 1992 and plateauing in a few years, as you would expect considering the use of the technology associated with the term. On the other hand, there are no recorded examples of "an UNC path" whatsoever.