There's no single answer to this because the term "technical class" is not well-defined historically. One could look to dozens of origin points throughout history — the people who developed and maintained the massive irrigation systems necessary for the early Urban Revolution, the Mandarins who expanded the Great Canal in the Song dynasty, the rise of mechanization in Europe even before the Industrial Revolution, the Industrial Revolution itself, etc. It gets especially messy depending on your definition of "technology" — do craftsmen count? (Which includes not just the weavers and the artists, but the blacksmiths, proto-metallurgists, alchemists, etc.)

Technological systems have been core to large human societies since the Urban Revolution around 15,000 years ago. They are, it has been argued, totally core to the creation of what we like to call civilization. We tend not to think of some of these early endeavors as "technology" (especially since they have almost nothing to do with what later becomes "science" — any definition of "technology" as "applied science" is relatively recent in human history), but by any standard they are that.

There have always been people who have maintained and created such technology, though the roles, training, and mindsets of such people (and whether anyone bothers to write down their work in history books) varies by society.

To posit that they belong to some distinct class, in my view, sort of puts the cart before the horse.

(On technological systems in human history, you can go worse than James McClellan and Harold Dorn, Science and Technology in World History, which is the textbook I use for my survey course on the history of science and technology.)