Question

In the cosmological argument, one of the rejections of an eternal universe is roughly as follows (as I understood from the booklet):
Just as everything in our world requires a cause, so too the universe requires a cause. If you say the universe is eternal and there is an infinite chain of causes going backward, that is an infinite regress. If you say that the universe as a whole has something beyond its particulars that makes it not need a cause—I would call that something God (though there is also a problem with that, since it is rather pantheistic, and we are Jews, right?)

I will try to reject this reasoning from a few directions.
A. On an ordered infinite regress
The Rabbi has referred several times to the principle that an infinite regress of causes is basically meaningless, since it is more an evasion of giving an answer than an answer in itself. I agree, but I think this needs qualification.
Obviously, if we ask a child who broke the window, and he says it was the monkey that escaped from the moon, where a spaceship had arrived… and so on with infinite excuses—it is obvious this is nonsense. He is inventing each excuse on the fly and dodging giving an answer rather than really answering. For cause A he gives cause B, for B he gives C, and so on, each time inventing a new excuse. Clearly that is nonsense.
But what about an infinite set of excuses that has an order to it? Like the egg that came before the chicken, which came before the egg, which came before the chicken.
The main difference between this series of excuses and the child's series of excuses about the window is that even though there are infinite excuses, there is an order in the excuses.
The real and fundamental problem in an infinite regress, as I understand it, is that instead of finding order and understanding the law and pattern for the cause of a given thing, what we get instead is a chaos of nonsense. But what about an infinite series when that infinity has a rule? The series is infinite, but the order is preserved. Like an infinite line—we cannot describe the line and tell you all the points on it, but that does not bother us, because the equation (= the "rule/order") of the line gives us the ability, at any place on the line you want, to tell you all the points.
So too with the egg and the chicken—even though there are infinitely many causes here, since we know them all and we know the series, the order is preserved, the chaos falls away, and the cursed regress is not here. Even though there are infinitely many causes, that does not bother me, because there is infinity within this order.
If you say (and you probably will say) that there is a problem with this argument because in the end, if you ask me what the cause of the chicken is, I will not really answer you, since I would now have to state this entire infinite series for the explanation to be acceptable. And since that is impossible (because it is infinite), then in fact I have not given an explanation for the chicken, and the original question returns.
I do not really agree with that claim, because implicitly it refuses to accept eternalism. Basically, when you ask what the cause of the chicken is, you can ask that in two ways: a) what is the direct cause of this chicken; b) what is the overall cause of this chicken. For a), the answer is obvious. For b), the answer is that there is none! That itself is the claim of eternalism (roughly speaking)—there is no first cause!
I will try to illustrate this with a two-dimensional circle of causes.
What is the cause of a given point? The point before it. And what is its cause? The one before it, and so on to infinity. And if you ask what the first cause is—there is none! There is no beginning in a circle! And if that is hard for you to accept—that is your problem. I do not have a problem here of chaos involving a cause emerging out of nothing—for every cause there is a cause. But what is the cause? You assume there is such a thing, but maybe reality is not actually required to be like that.
And likewise with the egg and the chicken—for every egg and chicken there is a cause, but what is the cause? Is it some alpha-chicken? No! That itself is the claim of eternalism: there is no beginning.

B. On the universe and the reasons for its particulars
One of the arguments against an eternal universe is that just as every particular in the universe requires a cause, so why should the universe itself not require a cause?
This requires examination. What do we mean when we say that everything in the universe has a cause? We mean that if we landed on Mars and found a car there, it would be absurd to say that this thing has no cause, and that it simply grew there on the trees a million years ago. Clearly such a thing requires a cause.
But we would not ask that about stones, right? We do not think—or are not so bothered by—the question of the original cause of matter itself, in the way we are bothered by the original form of matter.
And now for the principle: every form of matter in the universe needs a cause, but the universe itself—the prime hylomorphic matter—is itself not in need of a cause, and about it there is no problem saying that it is eternal.