It was often neither intuition nor improvisation, but rules. Bill Hammack's "The Things We Make" goes into a number of examples.

For a slightly more modern example, take European Gothic Cathedrals. People weren't guessing, they weren't improvising, and they weren't relying on intuition - if they did most of them would have collapsed long ago.

These structures were made without blueprints, and often many of the head masons may have been illiterate, but a knowledge of forms and rules such as "the thickness of the wall of an arch should be a bit more than a fifth the span of the arch" allowed for reliably producing stable structures.

These rules were less precise than modern engineering math and mean that many of the structures are overengineered / have higher margins of error than are considered necessary in modern construction, but they are not based on intuition or guessing.