Typically when you have a crappy argument, you need to spend a lot of time focusing on the some part of the argument that you can establish, so no one recognizes the huge flaws in the rest of your argument. Suppose you are arguing that there is an afterlife, and you have some empirical evidence for near-death experiences that cannot yet be explained in natural terms, you emphasize the failure of scientific explanations and skip quickly past the part of the argument that because we do not know why humans have some experiences, those experiences must be supernatural. Ross utilizes that argumentative strategy in the bulk of this book. He spends most of his time playing up the evidence for a Big Bang and a beginning of the universe and neglects to show how this evidence proves the existence of God. Perhaps because he thinks it is obvious, but I think this is how he thinks the argument goes.
1. Everything that has a beginning in time must have a cause ("a beginner" he says).
2. The universe had a beginning in time.
3. Therefore the universe must have a cause.
It's not clear that the first premise is true. On the quantum level, some events occur without a cause although there are probabilities that some such event will occur. However, the main problem with this premise is that since time only exists when there is matter, the universe had a beginning in time but could not have had a cause because there was no time before the beginning of the universe in which the cause could have occurred.
We can see the problem with this argument by noting that if there was a beginning in time, then God must have had a beginning in time, and, according to premise 1, must have a cause. Yet it is absurd to think that there is a cause of God's existence. Hence, the first premise of Ross's argument must be false.
Weirdly, Ross recognizes that God cannot have caused the universe by preceding it in time as we understand causation to work but "predated" the universe in a different time dimension. This is both meaningless and special pleading. It is special pleading because Ross specifically ridicules others who propose ways in which the universe might have existed before the Big Bang yet he appeals to such a "time before time" for his own hypothesis. Moreover if it is possible for there to be additional dimensions in time in which causes can occur, then there is no reason to think that the universe has a beginning in time. So, with no beginning in time, Ross's entire argument for the existence of God, based on there being a first moment in time, is unsound. In that case, the second premise in the argument above is false on Ross's understanding of this other dimension in time.
It's no wonder, then, that Ross spends most of his time on the evidence for a Big Bang. That can be supported with evidence. And, importantly, this gives Ross's argument a veneer of scientific respectability. But the further argument cannot be, and he spends almost no time discussing the argument above, and so does not address the obvious problems with such claims.
Ross does rely heavily on the authority of scientists, especially with respect to belief in God. It is always possible that his quotes are mined--taken out of context to appear to show something other than they actually mean--but it's possible that some cosmologists believe in God. However, it's not likely that Ross really wants to consider scientific authorities as counting for or against belief in God since scientists generally are much less religious, and the higher the status of the scientist the less religious they tend to be. Here's a brief description of a 1998 study of elite scientists, members of the National Academy of Sciences and their relative belief in God. They found that 7% of NAS members had a personal belief in God while 72% personally disbelieved. If Ross wants to play dualing scientists, using some potentially undistinguished scientists chosen only because they agree with him, against the survey of the most distinguished scientists in America, he will lose convincingly.
In sum, Ross spends a great deal of time reviewing the research on cosmology that supports a finite universe with a beginning in time. Then he turns around and hypothesizes that there is a time before the beginning in order to allow God to have created the universe. Thus, the argument he presents undermines the conclusion he wants to derive from it.