Thank you for touching on something that I've been wondering about for a while. I've never studied physics (or other hard sciences) but I've been forming the impression for a while that much of what gets publicized as "scientifically possible" is merely "not mathematically impossible" and that the two concepts, which to me seem far apart, get blurred, and that it's not by accident.
As I mentioned earlier, I taught physics at the high school level. I also taught an intro college course on the subject. Some of my colleagues had a nickname for me, “the experimenter”. That was because I was always asking about the experimental evidence.
That nickname was not meant as a compliment! The implication was that I was not “theoretical” enough. I found that odd, and also a bit amusing. All of science is built on experimental evidence.
If there’s no hard evidence, it’s not science. A good example of that is with climate change. The hard evidence is just not there. So it ain’t science.