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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Okay, despite what everyone almost everyone else is telling you, the fact of the matter is that engineering before modern computing was a combination of experience and effectively estimation.
The reason there are ancient structures which are big and impressive that have survived is that those were the ones that actually were designed well enough to survive. That is either because it was pretty easy to design them (like the Pyramids, which are literally just big piles of stone), or because the people who were designing it had a lot of prior experience to draw on, including experience they learned from books and from studying other surviving structures.
Fundamentally, the design of large structures before roughly the mid 1800s was informed guesswork. It’s true that there are a bunch of cathedrals that were built in the 1200s or the 1300s that have still survived. It’s also true that there were a bunch of cathedrals that were attempted to be built around the same time frame which collapsed during construction or afterwards.
It took until about the 1800s to the early 1900s for the disciplines of civil and mechanical engineering to move from this experience / rule of thumb design strategy to mathematical design. It took that long for stress and strain in materials to be understood well enough to be useful in actually predicting structural failure, and to be adequately proven. This basically didn’t happen until large scale structures stopped being built with masonry and stone, which had well-developed rules of thumb and began being built with metals.
As far as how people did things before electronic computers existed, the answer is that they made a lot of simplifying assumptions to make the math they had to do by hand tractable, that is, accomplishable in a reasonable amount of time. And then they applied factors of safety to account (hopefully) for all the simplifying assumptions they made and factors they may not have considered. And even after applying those factors of safety, it wasn’t unusual for things to collapse. Nobody could possibly sit down and do a detailed structural analysis of a modern 10 or 20 or more story building by hand, whether that was 100 years ago or today.
Engineering today with computer aided design is much better than it used to be. To be clear, better doesn’t mean safer, necessarily. Better means that the engineers who are doing the designing have a much more detailed and realistic understanding of what’s going on. Instead of having to use rules of thumb and large factors of safety, they can have reasonable confidence in being able to meaningfully understand what’s going on throughout a structure. That allows them to do a better job of engineering, which is accomplishing the necessary job by using a few resources as possible.
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