I've been thinking about this, and it may sound very ludicrous (and it probably is), but I may have come up with a proto-explanation for it. I hope I won't come across as some misinformed perpetual motion dummy.
Ok, so basically, people are puzzled because of the Universe's highly disordered state shortly after the Big Bang, which was the result of a highly ordered singularity suddenly exploding, resulting in chaos and tons of other material scattering around. Now, this should logically result in high entropy, but on the other hand, the Universe had unusually low entropy at its beginnings.
Could it be that the disorder present at that time was so disordered that it somehow looped back to ordered once again? After all, high entropy is more than just disorder, it is also a sign that the energy present within an enclosed system is also highly degraded and pretty much unusable and impossible to harness. It would make sense for the energy present at the beginning of the Universe to somehow be conserved within the particles scattered by the Big Bang, therefore allowing its harvest and use for the processes that eventually resulted in the Universe as we know it. I don't really know how such a system could be so disordered it eventually resulted in a triumph of order, but I think the high presence of usable, not-degraded, and conserved energy could be the key to that.
Does this sound in any way plausible? You can maul me if it's wrong, and if this problem has already been solved, well, I apologize for wasting your time.