This question has several major thinking flaws embedded in it.
The first is in the title, where you use "supernatural" as an ontological category. (others include the mistaken idea there are "Laws of nature" rather than hypotheses and theories, plus regularities, and the presumption that physicalism is the default view of the world and should be presumed until overturned). Back to Supernatural. What is "supernatural" ontologically? What is "natural" ontologically? These are terms with no useful meaning.
If you try to define natural ontologically in terms of physicalism -- you quickly run into Hempel's dilemma -- nothing can be excluded from future advances in physics, including Gods. You also run into the problem of philosophy which destroyed Logical Positivism -- physics needs philosophy to precede it, to establish the scientific method, and the metrics/criteria it uses -- and none of THAT is physics but must exist for physics to exist.
The only useful meaning for "supernatural" in philosophy is its epistemological usage -- the category of things for which one cannot use methodological naturalism to investigate. Some theists assert that God is in such a category, hence if one uses this epistemological definition, AND assert God to be epistemologically supernatural, THEN by simple derivation, one cannot provide "evidence" for God.
However, as Sam Harris argued extensively in The End of Faith -- in practice basically no theists treat God as epistemologically supernatural. Theists hold by their religious views for reasons, and these are most clearly on display in the debates BETWEEN different factions of theists.
Outside theists, the most common claim of epistemelogic supernaturalism I have seen is the "New Mysterians" among philosophers of mind. They hold that consciousness is intrinsically beyond our ability to understand, and it will always remain "mysterious". Note these are mostly physicalists, or physicalist leaning philosophers, who are explicitly arguing for part of our world being supernatural.
If you want to understand the reasons for theistic faiths, then you would be best off actually reading the evidence cases that theists put together, rather than asking other atheists to regurgitate straw man arguments against theism. Have you actually read any such arguments?
Many of the evidence cases put together by theists -- tend to establish the plausibility of their worldview, rather than its definitive truth. Among the best authors I have encountered in this set of writers are JP Moreland, Richard Swinburne, John Pokinghorne, and Paul Davies. The first three are Christians, Davies is a deist.
You also misunderstand the nature of evidence in methodological naturalism. NO evidences can EVER be definitive. Quine pointed out that theory is ALWAYS underdetermined by evidence! Therefore any hypothesized worldview or assumptions set is infinitely klugable to account for even the most embarrassing observations. There is also no "default view" that a competing one has to overcome before it can be accepted -- all worldviews or claims must make their cases against all evidence.
Because of the infinite klugeability of hypotheses/worldviews, the metric for goodness of aq theory or claim in the face of challenging evidence is not "can this evidence possibly be interpreted differently" but "how useful is the assumption set/worldview after it has been kluged to fit this evidence". The best theory I have found in Philosophy of Science for how this is done is Lakatos' Research Programme methodology. https://bertie.ccsu.edu/naturesci/PhilSci/Lakatos.html Another very useful framing is to describe the accumulation of a usefulness case for a worldview or hypothesis to be that of consilience https://science.jrank.org/pages/7591/Consilience.html
What one discovers, when one pokes, prods, and challenges a philosophic worldviews aggressively enough, it that every one of them provides incomplete explanations and justifications, and has incoherencies embedded in them. This is not sufficient to dissuade philosophers from holding by those worldviews. For instance the problems I noted for physicalism have not prevented physicalism from being the predominant worldview of Western philosophers for the last century. This is because philosophical worldviews ARE Lakatosisn Research Programmes -- and they accept the incompleteness of their current solution.
For me, a theist of a sort, my evidence base for accepting theism has been
the superiority of spiritual dualism as an explanation for consciousness over all physicalist, idealist, and neutral monist models.
The large supporting evidence set of "supernatural" experiences (I am using the term colloquially, not either ontologically or epistemologically) of direct apprehension of ghosts, synchronicity, and warnings.
the supporting evidence set of successful parapsychology experiments, which presume either dualism or idealism. https://parapsych.org/articles/36/55/what_is_the_stateoftheevidence.aspx
the extensive history of mystic experiences, where humans communicate with and interact with a spiritual universe.
My own success in doing so, following a process developed by a Gnostic: http://www.bswett.com/1990-03TwoWayPrayer.html
the direct experiences of a God in two way prayer.
This is a set of evidence compiled as part of methodological naturalism. It is a highly useful and effective worldview in navigating the world, and holds up far better to philosophic challenges than any other I know of. This is a consilience and progressive research programme case for a form of theism (di-theism).