There's a very common misconception among theists (and even among some non-theists) that science is strictly naturalistic. In other words, that science asserts that every phenomenon must have a natural explanation, and rejects any supernatural explanation out of principle.
This is incorrect.
It's true that science rejects supernatural explanations, but the reason is not philosophical or "closed-minded" stubbornness. No, the reason is purely pragmatic.
You see, a supernatural explanation is completely useless and serves no purpose. It's a non-explanation. It's exactly the same thing as saying "this phenomenon that we can observe can not be explained" (in other words, the mechanism that causes or produces the phenomenon cannot be physically observed, measured or tested.) "Cannot be explained" is not an explanation at all.
It's also a contradiction of concepts. If something affects the natural world, then by definition that something is itself natural. This is because if it has an effect on the natural world, then it can be observed and measured by said natural world, which is the very definition of "being natural."
The very concept of "supernatural" is ill-defined. If we can observe it in some manner, it's by definition natural. If something were truly supernatural, then it would be impossible to detect by natural means. But if we cannot detect anything supernatural, how can we tell if there is anything supernatural in the first place? What would be the difference between something supernatural that we cannot detect, and nothing supernatural existing at all?
Some people try to define supernatural as "not in or bound to this universe." But if there is something out of this universe, what exactly makes it non-natural? Especially if it can have an effect on this universe. (Again, if it can have an effect, it's by definition natural. Granted, it would be somehow different from what we observe inside our universe, but being merely different doesn't make it "supernatural.")
Even if there were something that could change or break the laws of nature (inside our universe) that in itself doesn't make it "supernatural." It would just be another natural phenomenon. (There's nothing that says that natural laws must remain constant everywhere and at all times.)
Shrugging off a phenomenon by attributing to a supernatural cause is useless and serves no purpose or meaning. Thus there's absolutely no reason to do so.