New atheists invoke 'science' as the pinnacle of methods to find truth.
In fact, atheists of a positivist inclination assert that science is the only way to know truth. By science, they explicitly mean methodological naturalism. Implicitly, they presume philosophical naturalism.
But what is 'science'?
Traditionally, as understood by philosophers from the ancient Greeks to the scholastics, scientia was Latin for "knowing" and "understanding". Scientia was an organized body of knowledge. It did not refer only to knowledge of nature. Theology was scientia. Ethics was scientia. Knowledge of nature was referred to as natural philosophy.
From the early modern period, science came to refer to scientia of the natural world. It has generally been distinguished by the scientific method-- a system of testing hypotheses about the natural world. Science came to mean primarily the acquisition of knowledge about nature that permits the manipulation of nature.
Understanding nature is, of course, still philosophy. It is still a kind of knowing. Scientia of nature, understood classically.
Science is stipulated to be the study of nature. So, of course, it cannot adjudicate the existence of the supernatural. It is a way of knowing tailored to knowing nature. And science understood as metaphysical naturalism does not presuppose natural causes. It presupposes natural effects. Supernatural causes are very much in the purview of natural science, as long as they have natural effects. An obvious example of a natural effect with a supernatural cause (by definition!) is the Big Bang. Nature itself cannot be caused by nature.
The question as to whether nature is all that exists is a question beyond science. It is a philosophical question broadly. It is a metaphysical question specifically.
From metaphysics, the argument that nature is all that exists is extraordinarily weak. Only two metaphysical arguments of any substance at all have been advanced to defend the assertion that nature is all that exists.
Hume proposed that perhaps nature, not God, is the ground of Being. If one must stop in causal regress, why not stop at nature, instead of God?
The reply to Hume preceded Hume. Scholastics had pointed out centuries earlier that the ground of existence must itself contain the principle of its own existence. It must not be contingent. But nature is contingent. It changes constantly, and its components begin and cease to exist continuously. In fact, we now know that nature (the universe) had a moment of beginning. It could not be its own cause of existence because nothing can cause itself to exist. Existence must be caused by Something outside of nature. That Something must Itself have an essence (what It is) that is existence (that It is). The Cause of nature must be outside of nature. Supernatural.
Kant understood the power of this argument, but he denied that we can extend logic to the supernatural. He asserted that all that we can know is the reality presented by our senses- the phenomenal. Reality-in-itself-- the noumenal-- was unknowable to us. he did believe in God, but he believed that God could only be known through the moral law in each of us-- the Categorical Imperative, but not through logic.
There are two problems with Kant's reasoning. The first is that the inference to the Prime Mover/First Cause/Necessary Existence is a deductive argument that extends only through the phenomenal-- through the world as known to the senses. The Ground for Existence is the conclusion of arguments restricted to phenomenal premises. We can validly infer that a Ground for Existence must exist based solely on phenomenal arguments. The nature of the Ground for Existence may be noumenal, but its necessary existence is demonstrable. The argument is phenomenal, and valid.
The other problem with Kant's critique is that if we understand the Ground for Existence as entirely beyond human understanding, including the conclusion that such a Ground exists, then we violate the Principle of Sufficient Reason (the PSR). The PSR asserts that everything has a reason for its existence. It of course does not assert that we currently know the reason for everything (we obviously don't), but it asserts that a reason for everything does exist.
If the Ground for Existence is Kantian noumenal, and intrinsically unknowable and beyond confirmation of its existence, then the PSR is violated. But is the PSR is violated for the universe, then it is violated for each component of the universe. If nothing in the universe needs a reason for its existence, then science and logic are without foundation. 'It just happened' becomes an acceptable explanation for anything and everything.
If Kant is right, then the reasoning Kant used to arrive at his conclusion is without ground. Kant's argument is ultimately self-refuting.
The atheist may reply that the need for a Ground for Existence must apply to God Himself, and therefore recourse to the supernatural doesn't spare us infinite regression.
The atheist would be wrong. God is supernatural, and therefore not a "thing" in need of explanation. If fact, only a supernatural Ground can stop infinite regress. God's essence is His existence.
Science is the study of nature using the scientific method. It has no traction on supernatural questions.
Metaphysics, which does have traction on questions of ultimate reality, provides a powerful and thus far unrefuted argument for His necessary existence.