It is becoming increasingly clear that Ross has no viable argument for the existence of God. However, in these chapters Ross "critiques" the views of contemporary physicists on the origin of the universe. Chapter 11 is on Hawking's A Brief History of Time.
Ross chides Hawking for failing to rely on the Bible when Hawking attempts to answer the questions, "What is the nature of the universe? What is our place in it and where did we come from? Why is it the way it is?" Yes, it's better to rely on the holy book of group of a nomadic shepherd culture from thousands of years ago than it is to rely on the results of the most advanced scientific research available. As much as I am trying to, it is sometimes hard to take Ross seriously.
What description does Ross give of Hawking's claims and arguments? And what is his specific critique of Hawking?
It's hard to know what the criticism of Hawking is because he does not really explain Hawking's position, deciding instead to quote a criticism from Hawking's ex-wife of Hawking's lack of traditional religious belief. All I could glean from Ross is that Hawking believes the universe might be bounded in time without having a beginning. Clearly if this makes sense, then Ross has no argument for the existence of God. Perhaps Hawking thinks that "Beginning" implies that one thing did not exist at some time and did exist at a later time. If that is so, then the bounded universe theory does not imply a beginning of the universe.
I'm not sure whether this is what it means for something to have a beginning. It might be that the fact that there is an earliest moment in time is enough to imply a beginning. Either way it is not the case that there could have been an antecedent cause.
Rather than try to explain or address any of this, Ross criticizes Hawking on the totally irrelevant issue that Hawking claims, apparently, that we can know eventually all the facts there are. Ross notes that Godel's incompleteness theorem (assuming we are formal systems which Ross probably does not think) and Heisenberg's Uncertainty Principle limit our possible knowledge. Further it is impossible to solve problems about certain physical systems. This issue is, of course, totally irrelevant to claims about God's existence. Ross is just taking a cheap shot when he cannot make any real argument against Hawking's theory. This is a bit like saying, "Yes, Mr. Einstein, that theory of relativity is intriguing, but you said that God does not play dice with the universe, and I'm fairly certain that God, being a nonphysical being, does not have any dice to play with. Booyah!" I am no expert on Stephen Hawking or physics, but I think he knows about these problems. Perhaps Hawking should be taken to mean that we can know everything within some understood theoretical limits.
In sum, Ross's chapter on Hawking is laughably thin. It's a criticism of a view that he doesn't even explain, and much of the criticism is about issues that are not relevant to the claims at issue (the need for a God to explain the existence of the universe).