If there is such a discrete boundary does it mean that a child could be somehow fundamentally different from its parents?
I guess the boundary is a bit fuzzy.
But I think, yes, child could be fundamentally different from its parents. I subscribe to the point of view that evolution occurs through random genetic mutations reinforced by breeding. So there will be the occassional mutation where the brain gets bigger and if that works out well for the individual, they get to reproduce. I'm sure you know all this!
When sufficiently complex brains first developed, i don't think those animals/people with them were instantly having all manner of strange thoughts, because a lot of thought and emotion and so on is taught. So to begin with, they would've just had the small advantage of being quicker-witted, having a better memory etc. At some point someone would learn how to imagine counterfactual outcomes of actions without actually trying them. By the time this happened, larger brains would probably already be the norm in the society and they could teach these techniques to others.
This is pure conjecture on my part of course.
But I imagine the "hardware" (big brains) would evolve first, just giving a qualititive evolutionary advantage to start with, and the "software" (imagining counterfactuals, self symbols etc) would develop later.