This is a tricky sort of thing to answer because of the nebulous difference between "empirical knowledge" and "theoretical science." They clearly blend into each other. But if one wanted to generalize, it is only from Descartes onward that you start getting self-described scientist-types who are interested in generalizing algebraic "laws of nature" ("theoretical science") of the sort we recognize today, which could be applicable in the same way that "engineering rules of thumb" ("empirical/tacit knowledge") had been for many millennia. You start to see people like Christopher Wren applying theoretical understandings of arches (developed by people like Robert Hooke) in England in the 17th century as well. So un-suprisingly (I suppose) you could date this to the Early Modern period, the apex of the so-called "Scientific Revolution" in the West, though I suspect these techniques did not become widespread until sometime later.

But again, I would hazard drawing some kind of special line here. Engineering rules of thumb are not necessarily quite the same thing as an attempted algebraic "law of nature," but they are not just trial-and-error affairs either. I would see this not as a "never done before" sort of thing, but more of a shading of importance and inclination. Wren is commonly used as the first architect to have a strong understanding of the physics of construction (statics), but it is not like everyone before him was just throwing things up without any principles. It is also worth emphasizing that our knowledge of these principles is not always complete — the guild-like approach typically taken by construction designers often emphasized secrecy and unwritten knowledge, and such things tend not to make it into the written record. (And even Hooke, for his part, was afraid enough of priority issues to not always publish his complete understandings, either!)