Well, I don't think that complexity "is all you need". "All you need" for what, anyway?
I think I understand what you mean by human exceptionalism, but I think it's besides the point. We don't even understand the intelligence of unicellular organisms, or insects. We have no "AI" that's half as smart as a cockroach.
The point is, there was never anything consequential that we invented, or discovered, all by chance. People always had some understanding of how things work, even if it wasn't understanding in the context of modern science, so even when it was only empirical knowledge, not formalised in the language of mathematics; even if it wasn't full knowledge, and yes, there are still many things we don't quite understand today. Off the top of my head, if I got that right, we don't understand exactly why or how anesthesia works. And yet, we have trained professionals who study and practice anesthesia, and they generally manage to avoid killing their patients, most of the time.
Unfortunately, we have nothing like that about intelligence. There's people studying the subject, coming at it from many different points (insect intelligence, IQ metrics, psychology, neuroscience, what have you) but there is not a body of knowledge that we can apply practically to show how intelligence works, and what happens when we do this, or what happens when we do that, to it.
Which means, if we do achieve "AGI" or whatchamacallit, at the present time it's not going to be because someone knew how to do it, but because someone got really lucky (or unlucky, perhaps).