Exactly. There were 430 crew members aboard the Enterprise during "Space Seed." Just because Chekov wasn't assigned to the bridge yet doesn't mean he wasn't already posted elsewhere on the ship during that incident.
We don't actually know when Chekov joined the crew, only when he started showing up on the bridge. From the evidence, we can deduce that he came aboard sometime after "Mudd's Women" (since he doesn't recognize Mudd later on) but before "Space Seed" (since Khan famously recognizes him).
For what it's worth, I made sure Khan met Chekov in the novels. Chekov assists in transporting Khan, his followers, and their supplies down to Ceti Alpha V in the days following "Space Seed."
Khan recognizing him is the mistake. He shouldn't have.