There are a lot of components needed for civilization. In the case of humans, agriculture was a big one, as it led to the feasibility of cities and specialization of labor. Absent specific adaptations to agriculture, tool making is essential for it. Advanced civilization is greatly helped by written communication (although human history shows we can get pretty far without it), which again depends on tool making. Without the ability to make tools there is only so far a species can get.

Human superiority also depended on non-intelligent traits. Without evolving the ability to sweat, we might never have had the opportunity to develop civilization.

Regarding brain size, larger animals need larger brains just control their bodily functions, so looking at brain size without controling for body size does not tell you much.

If you look at brain:body ratio, humans are pretty high up, but not a crazy outlier [0] (figure 7.13), and not the best [1].

A simple ratio probably not the best test, and seems to favor small animals. A more advanced measure exists [2], but suffers from a bit of a fine tuning problem.

There is also an implicit assumption that "intelligence" is a single dimensional value, which is simply not the case. For instance, beyond being a tool for communication, language seems to be a tool for thinking as well, but is clearly not a result of a general "intelligence" we have. Our overall intelligence is likely the result of a bunch of specialized systems within the brain

[0] https://lweb.cfa.harvard.edu/~ejchaisson/cosmic_evolution/do...

[1] https://en.wikipedia.org/wiki/Brain-to-body_mass_ratio#Compa...

[2] https://en.wikipedia.org/wiki/Encephalization_quotient