Among intellectual atheists, the most common argument against God's existence has to be Occam's Razor.
Definition of Occam's Razor. The most parsimonious explanation, all else being equal, is to be preferred.
The argument goes that a universe operating according to naturalistic laws with no creator is more parsimonious than a universe sustained by a creator, so therefore (again all else being equal, assuming that there is no evidence of miracles or special revelation of God to humanity) atheism is to be preferred to theism.
However, Occam's Razor does not necessarily apply to theism if one accepts the principle of sufficient reason.
Definition of the Principle of Sufficient Reason. Everything has an explanation, either rooted contingently on something else or by virtue of necessity.
If one accepts the principle of sufficient reason, then it no longer becomes the case that atheism is the preferred explanation for the universe, because intellectually consistent atheism entails the denial of the principle of sufficient reason.
The Christian apologist Leibniz believed that everything that could possibly vary has an explanation, and he formulated this principle as the principle of sufficient reason. So if the universe could have possibly not existed, which could have very well been the case, because it is not at all obvious why there should be something instead of nothing, then the universe must be grounded in something else, which in turn must be either necessary in itself or in turn grounded in some entity necessary in itself. Leibniz believed that the notion of a being who is necessary by virtue of its own nature points to the existence of God.
So if you ever meet an atheist who says that you should be an atheist because of Occam's Razor, respond with "No, because I believe in the principle of sufficient reason."