Originally, Khan was not genetically engineered at all. In "Space Seed," he was the product of controlled breeding:
SPOCK: No such vessel listed. Records of that period are fragmentary,
however. The mid-1990s was the era of your last so-called World War.
McCOY: The Eugenics Wars.
SPOCK: Of course. Your attempt to improve the race through selective
McCOY: Now, wait a minute. Not our attempt, Mister Spock. A group of
ambitious scientists. I'm sure you know the type. Devoted to logic,
I'm not sure if Star Trek II made it clear whether that was still the case. As of DS9 it appears that it's been retconned to have been genetic engineering, but I don't think there's a canon source indicating whether it was done before or after his birth.
EDIT: As Praxis commented, in Star Trek II, Khan had been genetically engineered. Not the first time Star Trek slipped a continuity cog, of course.