It just so happens that I came accross a rather interesting article the other day that indirectly deals with exactly this.
It concerned a mutation in the MYH16 gene. It is broken in humans and still functional in other primates. This gene controls the growth of specific sets of muscles. So as said, this mutation broke this gene in the human lineage at some point.
Here's one of the muscles that is controlled by this gene:
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Note how this muscles has shaped the skulls of the macaque and the gorilla. These are powerfull muscles too and it is easy to see how its continued presence would be a problem for brain enlargement. For the brain to be able to grow bigger, obviously the skull needs to accomodate for it. It needs to expand as well. The presence of that muscle, makes this accomodation very very difficult. Perhaps even impossible.
But it broke in humans. And somehow, this broken gene got fixed in the genome. This paved the way for skull reshaping and so many more things. Less powerfull jaw muscles also had important impact on life style. Less powerfull jaws = more difficult to chew certain kinds of food. This may even have played a role in why we started cooking food, as cooked food usually becomes softer and easier to chew.
It is very likely that this single mutation made our entire evolutionary path possible. That this mutation is what paved the way for our lineage to arrive at where we are now.
Having said all that, evolution is a gradual process. It's not like first it needs to develop a big skull which is half empty after which the brain can start growing to fill it up again.
It goes bit by bit.