First, the great majority of 'civilizations' [1] do not achieve anything like what the Incas did. Perhaps your perspective is distorted by survivorship bias - you know about the biggest successes, not the 99.999% that you've never heard of, like someone who thinks FAANG are typical of computer businesses. There are (or were until recently) societies in the Amazon, for example, no larger than a village and living in neolithic conditions. That is how far they made it. So there is the common question - why do some 'succeed' on such a large scale and some don't? Jared Diamond's famous book, for example, looks at this issue.
Second, the Inca did it with unique limitations: "Remarkably, the Inca managed to forge this vast society without the wheel, the arch, money, iron or steel tools, draft animals capable of ploughing fields or even a written language." That's from the OP.
It's mysterious to me that the OP spells out this question, but nobody in the discussion seems to understand it.
[1] I'm not sure that's the right word, but I'm not going to define it to precisely