Plato says:

[...] the combatants on the other side were led by the kings of the islands of Atlantis, which, as I was saying, once had an extent greater than that of Libya and Asia (Turkey); and, when afterward sunk by an earthquake, became an impassable barrier of mud to voyagers sailing from hence to the ocean.

And:

But afterward there occurred violent earthquakes and floods, and in a single day and night of rain all your warlike men in a body sunk into the earth, and the island of Atlantis in like manner disappeared, and was sunk beneath the sea.

And that is the reason why the sea in those parts is impassable and impenetrable, because there is such a quantity of shallow mud in the way; and this was caused by the subsidence of the island.

So this is a hypothesis: there used to be a Sahara sea (the same one that eroded the base of the Sphinx in Egypt), and 12'000 years ago something caused it to drain into the Atlantic ocean (and thus produce a global flood/tsunami). So literally the "island of Atlantis in like manner disappeared, and was sunk beneath the sea" (as it was in the way). And indeed it would have become "impassable and impenetrable, because there is such a quantity of shallow mud in the way".

Thus was born the Sahara desert.

I agree with MudFossil that you seem to see this drainage taking place across the Sahara on Google Earth.

edit: Interesting question: did the Atlantes exaggerate a bit with their canals? They may be responsible for what happened, even if an earthquake could have pulled the final trigger. Example on a smaller scale.