Unwilling to take the claims of scientists (or, more likely, the claims reproduced in the media and attributed to scientists) just on the basis of authority? Simple solution: get a scientific education in the field of your choice, build a lab, run the experiments. See for yourself. That way you don't have to take anything on authority. Unwilling to take the claims of religious people (or, more likely, the claims reproduced in the media and attributed to religious people) just on the basis of authority? Simple solution: start attending church/temple/mosque in a tradition of your choosing, develop a meditative/contemplative practice, immerse yourself in the writings and artistic productions of the tradition. That way you don't have to take anything on authority.

Standard answer: that question betrays a misunderstanding of what is claimed when one says that God exists in this context. When God is postulated as the origin of everything else in classical theistic philosophy, he's supposed to be a being that exists necessarily: i.e. it's not possible the God not exist. Asking 'Who created God" is like asking "Who made 2+2=4". In either case, the standard answer is that it's not a good question. If you say that we need to invoke God to explain the existence of contingent things (like the universe) but do not stipulate that God exists necessarily, then you are left with the problem of explaining God's existence. Now if Hawking's claim is that it is not necessary to postulate God to explain the rest of the universe, that does not imply that God does not exist. All it says is that if we want to explain why the universe exists, we don't need to make any claims about God. It's correct to say that this claim still leaves room for God's existence. There's nothing inconsistent about saying both that we don't need to invoke God to explain the law of gravity and that God exists. The interesting question is how we explain the law of gravity, if it's the law of gravity that explains the existence of the universe. From the linked article it seems that Hawking has decided to place his bet on an incomplete version of string theory to accomplish this:

"It is not necessary to invoke God to light the blue touch paper and set the universe going." In the forthcoming book, published on 9 September, Hawking says that M-theory, a form of string theory, will achieve this goal: "M-theory is the unified theory Einstein was hoping to find," he theorises.

The term of art for this sort of claim is the 'promissory note'. It's a version of the claim 'some day science will be able to explain [something it cannot currently explain]'. The Guardian article doesn't say anything about why Hawking has decided to repose confidence in this particular version of string theory, so we don't have the means to evaluate his decision. So: the story is that Hawking has decided to place a rather large bet on a version of string theory to, one day, explain the law of gravity and hence complete the explanation of why the universe exists. That idea doesn't have any particularly interesting consequences as regards God's existence or nonexistence. If Hawking is right, however, atheism will someday be able to justify itself scientifically without resorting to promissory notes. Sorry to be so non-inflammatory about this-- I teach this material for a living.