Stephen Hawking did not believe in God. I do not think anything of philosophical importance hinges on this, but since others have found it important enough to deny I think it is worth reviewing briefly.
If there is any doubt about what Hawking thought about whether or not there is a god, here is what Hawking said in a 14 March 2018 interview with El Mundo:
Before we understand [sic] science, it was natural to believe that God created the universe. But now science offers a more convincing explanation. What I meant [in A Brief History of Time] by “we would know the mind of God” is we would know everything that God would know if there were a God, which there isn’t. I am an atheist.1
And in the first chapter of his posthumous Brief Answers to Big Questions:
When people ask me if a God created the universe, I tell them that the question itself makes no sense. Time didn’t exist before the Big Bang so there is no time for God to make the universe in. It’s like asking for directions to the edge of the Earth—the Earth is a sphere that doesn’t have an edge, so looking for it is a futile exercise.
Do I have faith? We are each free to believe what we want, and it’s my view that the simplest explanation is that there is no God.
1 Transcripts differ about the tenses of some of the verbs in the first sentence, but you can just follow the link above to the interview and listen to the audio yourself.)