What would it look like? Something akin to the ‘scientific’ study of the unseen energy called Darwinism.
Scientists like Dr. Kevin Knuth (in the article) have been struggling with UFOs because they can’t be taken to the lab for empirical, repeatable analysis. Unfortunately for them, studying UAPs requires adapting scientific methods to phenomena that defy conventional experience.
I would think that such a study would need to combine three approaches: the rigorous standards of laboratory science—despite the absence of repeatability—the investigative breadth of forensic criminology, which identifies causes, patterns, and consequences while also applying empirical methods to all available evidence, and the thorough evidence-gathering of good old-fashioned detective work, which considers all valid evidence, whether material or circumstantial/anecdotal.
Beyond that, scientists would need the mindset of explorers venturing into unknown worlds and biospheres—open to discovering what they can’t yet imagine.
As an aside, I think the UFO matter is beyond the capacity of many scientists because they’re materialists.
I remember back in my early college days, I told my chemistry professor that I was fascinated by the scientific study of the human mind. He huffed and said something like, “That will never be science because it can’t be measured and studied under a microscope. That will always be quackery.”
We can see a bit of that same attitude when it comes to UFOs.