For me to properly evaluate Stephen Hawking's statement, I would have to know everything he knows. Which IMO is never going to happen. I don't read a lot of cosmology because of this. I just literally don't get how a universe can arise spontaneously from nothing according to the laws of science. So if I take Hawking's word for it, I am accepting an argument from authority.
I'm willing to do that, provisionally. But when I look at his qualifiers, I have other questions. Where did the laws of nature come from? Is this the only universe ever, or did others form under the same laws of nature, or perhaps different ones? I can't conceptualize of time starting with the Big Bang; I'm always worrying away at the boundaries ... what came before the Big Bang? What's on the other side of the universe? Even asking those questions shows I don't have Hawking's understanding.
Science doesn't and maybe can't answer those questions. So, sorry if this sounds like a cop-out, but because of my own ignorance, the scientific explanation is something I have to take totally on faith. A universe from nothing violates all my mental models, but even if I did have deep and broad understanding of quantum mechanics, I might still be left with questions. And so Hawking's words do not dispel the mystery for me; they actually enhance my sense that there are still deep mysteries humans may never be able to unravel. Perhaps due to my ignorance, I have a niggling hunch that some kind of creative/destructive force might underlie ordinary reality. And though I've never found a religion that matches my admittedly vague concept of that force, I haven't ruled out its existence. If the laws of nature spontaneously created the universe out of nothing, I'm in awe of the the mysterious origins of the laws of nature; and those words, "awe" and "mystery" IMO come close to describing religious feeling - which keeps me from identifying as an atheist.
To me, being agnostic seems like a tenable position, though some people say there is no such thing. I have never embraced a religion; I do accept that many if not all gods have been proved fictional; but I still believe there is room for me to say "I don't know" if any god exists.