Take, for example the example (of Lennox) that if y exists, then x should be its cause. What about X? Who or what caused it? We would go back to another cause and another ad infinitum. So monotheists would conveniently think of an uncaused cause or the unmoved mover or the prime mover. Is this logically correct? Are we side stepping logic? At one point, we have to abandon logic and side step it to prove God’s existence.
You articulate here a common misunderstanding of the view expressed by Lennox and others. There is not an infinite regress ("ad infinitum") involved, nor is the postulating of an Unmoved Mover arbitrary. Rather, the argument is as follows, and it *necessitates* an uncaused first cause to do the "moving," whether one is reasoning as a Naturalistic or a Theistic person:
That which has a beginning has a cause.
The universe had a beginning.
Therefore, the universe has a cause.
That's all simple logic, and not really easy to debate.
Premise one is the assumption of all science: things which start to happen do so because something caused them to happen. Any spacial-temporal phenomenon always has a cause. We may not always know what it is right away, but we know there will be one. If we don't accept that, we are simply rejecting science itself.
The second premise is based on the preponderance of actual evidence. Our universe manifests all the signs of having begun at a definite point in the past, such as explosive patterning and escape velocity in expansion. The current cyclical models or multiverse models are (so far failed) mental models only, and are at present neither testable or evidentiary. In any case, the multiverse dodge has its own rational problems (See my post on the article "Nonsense on Stilts," if you want more on that.) In any case, the best scientific evidence we have at the moment backs premise two, so reason tells us to back it.
Premise three is an inevitable consequence of premises one and two, so not disputable if the prior two are accepted. But this "cause" cannot itself be part of the chain of contingent events, since it is the thing we are expecting to explain the existence of all things; it must be, literally, "super-natural" in the sense of being above and beyond all our scientific laws and the chain of natural causes -- so as to function as the rational, causal explanation of how they came into existence. Were it merely a temporal cause itself, then the infinite regress problem would indeed apply.. but to both the Theistic and the Naturalistic explanations equally.
What this implies is that whether one goes with a purely Naturalistic first cause or a Divine First Cause, one is going to have to postulate the existence of something uncaused, since it has to be used to explain not only the existence of the universe but also the appearance of all the laws governing and applying to it. Admittedly, this stops short of proving anything about he nature of that First Cause; but the important point is that Naturalism does not get us out of positing an uncaused first cause. Both views end with such a claim.
I fail to see why any of this involves sidestepping logic. You can see it's a pretty straightforward syllogism, and it works very nicely. We may not learn anything from it about the *nature* of the first cause, but it shows there's nothing at all irrational about positing one. And for the nature of the First Cause, other arguments can be brought in to supplement. These will be deductive rather than inductive, but can still be offered in forms that are quite strong probabilistically. Since science itself only ever offers *probabilistic* arguments, to do so can hardly be held to be a flaw in Theism.
Finally, how can, as you say, "sidestepping logic" make it possible for us to "prove" anything? Is not the word "proof" a word that naturally implies the use of evidence and reasons? If not, then in what sense can we claim to have "proof" for anything at all? Or again, you say...
I think logic can never help us prove or understand God.
If by "prove" you mean "show beyond any possibility of rational doubt," then, as you say, that only happens in maths. But if by "prove" you mean "provide significant rational evidence for," then your claim seems unjustified: you'd have to dismiss all the rational Theistic arguments entirely, which you could surely only do if you actually refuted them (which you have not yet attempted to do, of course). But all you say above is that you "think" that "logic can never help," which is not actually much to ask of the evidence: any little bit of knowledge about God that comes from a Theistic argument would constitute "help."
But what about your second claim, that we can never "understand" God: do you mean "comprehend entirely"? If so, then of course you must be right: we could no more expect to understand *everything* about the Supreme Being than to drink Lake Superior, the largest freshwater lake in the world.
On the other hand, do you mean only "learn something about"? If so, then again I see no reason to think you're right about that. For while I might admit I can't drink Lake Superior, I can easily have a cup from it. I can't know *all* of God, of course; but that surely wouldn't mean I can't therefore know *anything* about Him. That just doesn't follow.
You may be right to say that logic will not give us the whole story; but is it then rational to suppose it can't give us any useful *part* of the story or function as an important aspect of our search for answers or as support of reasonable belief?
We may yet have important use for logic, even if the referent is God.
