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The problem I have with this entire line of reasoning is that it is ungrounded and hence of no utility. As an example, take this statement:
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I mean that the universe has not always existed. At some point it started to exist.
On the surface it seems like a reasonable statement, but it is a statement of the time history of the universe. The problem is that the universe is a spacetime structure so that without a universe there is no time. A statement along the lines of "at some point in time the universe started to exist probably has no meaning. If the universe exists within some greater structure we have no understanding of the nature of that structure. At this point in time we have no ability to test the properties of that structure experimentally so that theoretical discussions are unsupported. It is also very plausible that we will never have any ability to test that structure.
I do not see that a discussion about the origin of the universe can clarify anything. It is ungrounded speculation such that anything is possible.
My understanding is this: we can track the history of the universe back to just after the Big Bang. We don't know what happened at the actual moment of the Big Bang because classical physics breaks down at the density levels of the Big Bang and so we need a theory of gravity that works on quantum levels, which we don't have right now. However, cosmologists
have developed various models that purport to explain some of what happened. Some of these models postulate a universe where time began with the Big Bang (I think the Hawking-Hartle model is the most well-known of these). Others postulate a universe where time extends back before the Big Bang.
So you're right that whether or not time began with the Big Bang or not is a matter of speculation for now. Now, there is a semi-technical issue here, where William Lane Craig claims that the Borde-Guth-Vilenkin Theorem shows that any viable model of the universe must show that time begins with the Big Bang. I've not found any actual physicists who agree that this is an implication of this theorem, but insofar as there is an empirical claim by the proponents of the Kalam, it is that the BGV Theorem proves that time began with the Big Bang.
My objection to the OP, which never really got off the ground, is that the main problem with the Kalam argument is
not just that we don't actually know whether time began with the Big Bang. That seems to me one of the weakest objections. It is especially weak if you don't bother to show how Craig's interpretation of the BGV theorem is incorrect, or that his arguments against the possibility of an actual infinite also fail. In fact, it seems to me very plausible that it did begin to exist then! But I don't think that shows that the universe needs a transcendent first cause. Nor do I think that if we proved that the universe began with the Big Bang that suddenly all the cosmologists would become theists.
This is because I think that Carroll, Hawking, and other physicists are correct when they say that the idea of causation as we ordinarily understand it doesn't really apply to things like the beginning of the universe - especially because it relies on an older understanding of time that probably is inconsistent with modern scientific definitions. Thus, premise (1) is, in my view, the more serious problem with the Kalam argument. Premise (2) is an empirical claim, one that most cosmologists seem to believe is still open.