His intellect far surpasses that of any average human, because he's genetically engineered. This has been stated numerous times throughout both Space Seed and TWOK.
The point they were trying to drive in TWOK, was that Kirk only managed to beat Khan via his experience and the efforts of his crew. The fact of the matter is that Khan commandeered a starship, worked out how to use it, and then held his own against another starship with a formidable commander and bridge crew.
In one of the deleted scenes, restored for the DE, Kirk says to McCoy that the only reason they escaped the intial Reliant attack was because "I (Kirk) knew something about starships that he (Khan) didn't".
Consider this also, Khan is 200 years out of touch with science and technology. Even the near-twenty years that he spent on Ceti Alpha V, would have been spent with severely limited access to 23rd century technology. He could have learned a few things yes, but not how to operate a starship that is of a much newer generation of technology than the one he was briefly exposed to.
If it took him a day or so to accustom himself to a starship, the odds are that he would have eventually worked out the basic principles needed to reverse engineer the Genesis device.