What does "beyond the physical" even mean? I assume you mean something "supernatural," meaning something that is "true/real," yet impossible to study or even verify empirically.
I would assume they would be possible to verify in some way once we've reached the stage where hard AI is nearly achieved.
Biology is really not much more than a self-replicating subset of chemistry. Without evidence to suggest something sort of psuedo-supernatural difference between the simplest of single cell organisms and homo sapiens, I think the only reasonable position is that whatever it is that "preforms" intelligence falls under the realm of the physical sciences.
Until we acquire evidence to suggest otherwise, it is silly to assume anything else.
Longbets is fine, but such unfounded speculation doesn't have much use in serious conversation.
"proving the position proving the position"
It seems like you might be misunderstanding the role of science.
After that, it's just a question of engineering.
In particular I would be interested to hear what some of these phenomena are. See, the lack of a "concrete explanation" isn't really a useful thing to say about something. We don't yet have anything that could be called a "concrete explanation" of even things like gravity. What we do have are theories that allow us to make useful predictions about how gravity will effect things. Imperfect as those, like all, theories are, we've still put stuff on other planets with them.
There certainly are many "open problems" in science, but to my knowledge we have yet to ever encounter anything that is fundamentally beyond the grasp of the physical sciences. Take for example the Coronal Heating Problem: On the surface it seems to violate the 2nd law of thermodynamics (which is some rather heavy shit...) but even in extreme cases like that science solders on. There are numerous hypothesis that have been proposed to explain it, and over time our understanding of it will only become more robust.
Anyway: To address this particular concern I'd like to say that until we have any strong evidence to suggest that humans possess a more powerful model of computation than we already regularly reason about, we have to assume that they do not.
It's possible that there are hard limitations on our ability to recreate some of the very fundamental phenomena we experience in everyday life. Intelligence may be among them.
Every other natural phenomenon that doesn't obscure infromation that way can be figured out. There may of course be soft limits like it taking a billion years to figure out.
Anyway, comparing creating intelligence to creating gravity is nonsensical. I literally cannot make sense of that.
Serendipitously to you mentioning this now, only a couple of weeks ago they announced they have a good candidate for the explanation, which is Type II spicules.