"So how did intelligence emerge in humans?"
Is it the ability to learn from and thus react to certain stimuli? In that case pretty much the entire animal kingdom could be classed as intelligent.
Is is the ability to communicate with other members of one's own species? Still most of the animal kingdom there. Communicate complex and abstract concepts? Now we're narrowing it down a bit, but we've still got primates and cetaceans to account for.
Permanently record information such that other members of one's species can retrieve it even after the individual originator of the information has died? Ah, now we might be talking Homo sapiens. Reading, writing, drawing and painting allow us to transcend death by passing on our knowledge to our successors. Wait a minute - ants can also do this with smell trails. Ant smell trails inform other ants not only of a path to food, but also what kind of food it is, how far it is and how much of it there is. And it persists long enough for other ants to make use of it even if you kill the ants that originally made it. So that's out, too.
Control and manipulate one's environment to benefit one's species and/or oneself? Yes, humans can do this, but it's just a question of extent; a termite mound with it's moisture, ventilation and light control mechanisms is just one example of another species doing this. So that doesn't uniquely define human intelligence either.
Self-awareness? Nope - dogs, dolphins, chimpanzees, orangutans and many other creatures have also clearly demonstrated a sense of identity, being able to recognise themselves in mirrors and behaving in ways that indicate the presence of self-awareness in a group context.
In the end, one is forced to the conclusion that intelligence didn't "emerge" spontaneously, so much is it has always been present in some degree as a function of life. Likewise, computer intelligence won't just "emerge", it's present now, has been since the invention of the pocket calculator, and will continue to develop, grow and change. Intelligence isn't a "yes/no" equation, it is a continuum of behaviour that has no effectively determinable thresholds.