“Is any phenomenon that lacks an explanation, ‘supernatural’?”
No.
Any phenomenon for which conventions of physics or chemistry cannot be applied, due to the fact that the particular phenomenon isn’t subject to pertinent laws or principles, is supernatural.
In trying to figure out something like cancer there’s no reason to exclude known principles of physics and chemistry.
But in thinking about the moment of the Big Bang, conventional principles of physics and chemistry are useless. The rules of nature, as defined by conventional science, don’t apply.
If you think there are “different kinds” of supernatural, let me know what they are.
The problem with that explanation again relates to what Kosta50 exposed in his earlier reply to you where he pointed out that for you to accept David’s child’s being inflicted by a fatal illness by the supposed deity as “divine justice”, you have to resort to the same deity’s supposed words which essentially boil down to mean that it did it because it can do it.
Now, for someone to accept this as sufficient justification, it requires them to possess faith in this deity, beforehand. In the same manner, a Muslim can “justify” the vile actions of that religion’s god, as well - and many do just that.
What is your explanation as to why there is a remarkable ‘toning down’ in the attitudinal qualities of this divinity-figure, from the Old Testament god all the way through Jesus? In other words, is it possible for you to imagine, say, Jesus ordering the slaughter of the Amalekite infants?
Why must the effects of ‘supernatural phenomena’ be precluded from consideration in studies pertaining to diseases like cancer, particularly when diseases have been a mode of exerting influence by the divinity figure of your faith?