Dan Dennett has it right in his comments below when he puts the emphasis on acquiring language, not having language, as a precondition for our kind of consciousness. For what it's worth, I have some (likely unproveable) beliefs about why the preschooler's acquisition of a structured language is so important for all the rest of her higher intellectual function. Besides syntax, intellect includes structured stuff such as multistage contingent planning, chains of logic, games with arbitrary rules, and our passion for discovering "how things hang together."
Many animals have some version of a critical period for tuning up sensory perception. Humans also seem to have one for structured language, judging from the experience with the deaf children of hearing parents who are not exposed to a rich sign language during the preschool years. Oliver Sacks in "Seeing Voices" described an 11-year-old boy who had been thought to be retarded but proved to be merely deaf. After a year of ASL instruction, Sacks interviewed him:
"Joseph saw, distinguished, categorized, used; he had no problems with perceptual categorization or generalization, but he could not, it seemed, go much beyond this, hold abstract ideas in mind, reflect, play, plan. He seemed completely literal—unable to juggle images or hypotheses or possibilities, unable to enter an imaginative or figurative realm.... He seemed, like an animal, or an infant, to be stuck in the present, to be confined to literal and immediate perception..."
In the first year, an infant is busy creating categories for the speech sounds she hears. By the second year, the toddler is busy picking up new words, each composed of a series of those phoneme building blocks. In the third year, she starts picking up on those typical combinations of words that we call grammar or syntax. She soon graduates to speaking long structured sentences. In the fourth year, she infers a patterning to the sentences and starts demanding proper endings for her bedtime stories. It is pyramiding, using the building blocks at the immediately subjacent level. Four levels in four years!
These years see a lot of softwiring via the pruning and enhancement of the prenatal connections between cortical neurons, partly on the basis of how useful a connection has been so far in life. Some such connections help you assemble a novel combination of words, check them for nonsense via some sort of quality control, and then—mirabile dictu—speak a sentence you've never uttered before. Some must be in workspaces that could plan not only sentences but an agenda for the weekend or a chain of logic or check out a chess move before you make it—even be tickled by structured music with its multiple interwoven melodies.
Then tuning up the workspace for structured language in the preschool years would likely carry over to those other structured aspects of intellect. That's why I like the emphasis on acquiring language as a precondition for consciousness: tuning up to sentence structure might make the child better able to perform at nonlanguage tasks which also need some structuring. Improve one, improve them all?
Is that what boosts our cleverness and intelligence? Is "our kind of consciousness" nothing but structured intellect with good quality control? Can't prove it, but it sure looks like a good candidate.