Today's review of the Walgreens-exclusive Marvel Legends Mystique action figure spoke of how Dave Cockrum had designed the character before Chris Claremont decided to use her in the comics.
"This drawing was done for fun and hung in my office until my partner Chris Claremont wandered in one day, saw her, and started to drool. 'I want her!' he said. He named her Mystique, gave her powers and added her to the Uncanny X-Men rogues gallery."
So that's the true origin of Mystique. As a bonus, here's a Marvel house ad for Ms. Marvel, featuring her soon-to-be archenemy in the background: