Being a contrarian, I start with the end product — humans — and look backwards and say that the evolutionary process can’t possibly explain the creative nature of man, the intelligent designer.
What it comes down to, IMO, is that you probably don't
want an explanation.
I bet that, if for example the field of artificial life / artificial intelligence comes up with a way to make these "unique" human capacities appear out of nowhere, you will
never accept that it went like that in nature, too. You will insist that it is just a "simulation", a way to "mimic" natural processes, but in no way an accurate description of the "real" process.
Of course, any results in these fields would also come very gradually. So I also already predict that you will go through a process of continuously moving the goalposts further back.
Seriously: can you imagine ANY type of discovery that you would accept as the answer to your questions?