They had to know what materials to use, which alloys, load bearing weight of the materials, how to place and configure them, etc.
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Engineers figured out materials.
Engineering has been studied in universities since the Greeks in the west and the Ottoman Empire (maybe before) in the Middle East, and I’m not sure how long in Asia(China/india specifically, but more cultures than I want to name), but realistically several thousand years.
Many other cultures had a concept and practice of engineering, but not many had formalized university structures focused on engineering.
Many structures like The Egyptian or Mayan pyramids, Angkor Watt(as examples) are ancient and well engineered.
Computers figured out the numbers.
Computers used to be the catch all term used for a person figuring out the math of a problem. The movie “hidden figures” highlights some of these folks. In the 1960s many of these computers were women, or women of color as this job was seen as “beneath” men at the time.
So the short answer is: engineering and mathematics. All by hand. Sometimes chiseled into a stone, sometimes drawn on animal skins with charcoal. Lots of trial an error until something worked.
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