Ok. Let's take another look at time. And ignore for a moment what any author has to say about it. We can do a thought experiment that I think might elaborate my position better.

-If space was infinite, things could exist that were infinitely far away. I can agree on that.
-The number line has nothing to do with infinite time, because we're dealing with an infinite regress of cause and effect.

The number line is basically a hypothetical construct. And furthermore, 1 doesn't cause 2 and so on, so it really isn't a very good metaphor.

In order for my thought experiment to work, I think you'll have to throw away the notion that we do exist. Let's imagine away our present reality, and go to a time (assuming the big bang a priori) before the big bang.

In this 'pre-universe' state, we have an infinite regress of causes, but we don't know the final outcome yet because we can't assume our universe a priori or the experiment is contaminated (as well as illogical).

Let's call this infinite cause series ICS for a moment. In this ICS scenario, we have no initial cause, because whatever caused any given cause is preceded by an infinite amount of causes.

Furthermore, to simplify things, let's say that this series of infinite causes is just the same cause and effect leading to the same event over and over again. We'll call it event X. Event X1 leads to event X2 and so on and so forth.

Now, let's pick an arbitrary point on this series and call it event Xa. Event Xa is preceded by an infinite amount of causes. So we know that, no matter what, this event is preceded by an infinite amount of causes by nature. But something else we can assume by this Cause X is that it leads to an infinite number of Cause Xs. Event Xa will continue to cause an infinite set of Event X's for all eternity. We go a trillion years into the future and we run into an Event X again. We go a trillion trillion years into the future, and still more event Xs. Once again, we go an infinite trillion years into the future and we still run into yet another Event X.

You say that if the universe is eventually caused, then that solves the problem because even if there's infinite time, we don't have to wait for an eternity to exist. But if there is an infinite regress of causes, there will never be the effect of the universe. Therefore, we won't even get the chance to wait for an eternity. What I'm saying is that, if there is an infinite amount of causes for an effect, they'll never reach the desired effect.

If Event X were truly infinitely recurring, then it would never cease to 'recurr', and nothing except an event X will ever exist. This goes for any infinitely regressive pre-universe. If it were truly infinite, it will never cease to be anything except a pre-universe. If at any point it ceased to be a pre-universe, then in fact we would know it wasn't infinite.

If each step progressively leads closer to the universe from a 'lower' event, then it will have acheived the universe an infinite amount of time ago. Which means our universe would be dead right now because it would have existed an infinity ago. Any ascension in steps, since such ascension has no beginning, will have occurred so long ago that we would never even be able to go that far back in time. In fact, it would seem almost impossible to have occured at all.

Regardless of what's counterintuitive, I don't think there's any two ways around the problem. If you want to quote a devistating critique of this claim from that book, then please do. In the meantime, I see no reason to believe this is illogical.

Certainly, from your viewpoint, it makes sense. If we already exist, and there's an infinite regress of events/time, then we wouldn't have to wait an eternity. But if there were an infinite regress of events/time, we wouldn't even be here to consider the point.