Maybe it helps to be acquaintanced with science from an early age. Nature does have a tendency to organize itself into patterns spontaneuosly, in ways that to many people suggest a lack of a purpose or will "behind it all".
The thing with that is, if there was absolutely no purpose, existence itself would be chaos. If existence doesn't have a reason for existing, it was just the flip of the coin. Knowing that a property of things that exist is that it isn't chaotic, it would be strange if existence is chaotic itself.
But then you realize, at some level it IS chaotic. If there is a purpose to existence, there needs to be a purpose to that purpose, all of the way down. So instead of the 'turtles all the way down' joke, you could apply it to existential philosophy and say 'purposes all the way down'. But at some point there must be a meaningless, chaotic purpose. No matter how deep that point is, it makes existence chaotic on all levels. One might say all of these purposes are not formed consciously, but why not look as the actual information in the universe (the actual abstract, informational existence of everything) as a mind itself? It is very similar to a computer drive, and a human mind itself. It is the storage of information, the only difference is that a human mind has a select view of limited amounts of information, while the universe would exist as an objective view of all information.
Of course, some people might see that as evidence for some sort of creator God, perhaps for deism or panentheism. It ends up being quite an arbitrary call, though.
On a more practical level, patterns do not make for much of evidence for a deity, at least if we take deities to have moral or religious meaning.
Some patterns can't be described, only can be felt. For example, a person without ASMR would not be able to understand what ASMR feels like, even the description can make him comprehend it.
Many people clearly do. I often feel that it is a matter of esthetical inclination.
Does this mean you feel it's based on over-interpreting the beauty that appeals to some from nature?
If so, this isn't the pattern I'm talking about. It has nothing to do with how beautiful existence is. It has more to do with how strange existence is. It's very paradoxical, and many found that the deeper you look in at life, the less it makes sense.
I'm not quite that certain there is so much of a challenge of mutual understanding. But I will agree that it is probably not possible to argue one's way into convincing the other, at least not often.
So far, the only arguments I can imagine being said is; "It is just clear that God exists, look at the world" and "No, man, you're not looking at the world right. Look at the world again, it's obvious that God doesn't exist."