A commenter on another post brought up the cosmological argument, so here are my reasons for rejecting the cosmological argument. I’m going to be fairly brief, but keep in mind that I’ve read Swinburne, Craig, Aquinas, Aristotle, etc., so I know more about cosmological arguments than I will be using here.
A very simple form of the cosmological argument asserts that since everything has a cause, the universe must have a cause, but the chain of causes cannot go back forever, so there must be a first cause, which is God. The problem with this argument is that the first premise contradicts the conclusion – if everything has a cause, then there is no first cause.
A more sophisticated form of the cosmological argument says that everything that begins to exist has a cause, and the universe began to exist, so the universe has a cause. The problem here is that the universe did not begin to exist. Beginning to exist assumes that there was a time at which the thing that began to exist did not exist, and there was no time prior to the universe at which the universe did not exist, since time is defined in terms of the universe.
The theist might respond to this last point by saying that something begins to exist if there is a time such that it is not the case that prior to that time, the thing in question existed. The universe began to exist by this definition, because it is not the case that prior to the first point in time, the universe existed – after all, there was no time prior to the first point in time. The reply to that is simply that by that definition God began to exist as well, so we fall back into the infinite causal regress that the theist was trying to avoid in the first place.
Another form of the cosmological argument says that everything contingent has an explanation, and the universe is contingent, so the universe must have an explanation in something that is not contingent but necessary, and this necessary being is God. The problem here is that there is no way to explain what “contingent” means without begging the question. For example, we could say that something is contingent if it depends on something else for its existence, but then calling the universe contingent is question begging.
So, I don’t think there are any sound versions of the cosmological argument. Again, I’ve read a lot more than I’ve used here, but this should give you the basic idea of why I don’t think there are any sound versions of the argument.