We need a palm-to-forehead icon!
My understanding of what Hawking means is that he believes he understands enough about cosmology to explain how the universe came to be as it is without needing a supernatural "start". He sees no indication that a "god" has to exist, and therefore chooses to believe that "god" does not exist.
This is quite a long way from being able to state with certainty that "god" does not exist.
No one can be completely certain about the existance of "god", so chill out. Agnosticism* seems like the only really reasonable position to take.