^ Occam's Razor.
Another possibility. Zephram Cochrane's flight was the first known
successful warp flight, but there had been previous attempts. Either nothing happen, the ship was destroyed, or (in the case of the Valiant) the ship simply disappeared and not was heard of again.
Picard certainly regarded Cochrane as the first Human warp traveler, but the 24th century as full of important missing snippets of information from history. When Kirk met Cochrane, he refer to him as the discoverer of the space warp, not as the first man to travel faster than light.
Perhaps Kirk knew something Picard didn't.