Interesting speculation, in this article, that there could be a realm beyond space (or even space/time) that we think of as such a rock solid foundation to our reality.
I like pondering these type of things.
As for finding evidence to fit our current scientific paradigm, one small part of this speculation could be tested fairly easily. The concept of the Kaleidoscope discussed in the article. If we are in one of the glass pieces of the Kaleidoscope, who's image gets repeated, we could see if there are parts of the universe; like distant galaxies, that look exactly the same as other parts of the universe. Like mirror images.
I would guess our current astronomical technology is not refined enough to totally rule this out. I would guess that we see distant galaxies that look alike, but we can't yet see the finer detail as to whether they are mirror images, or not.
We do see mirror images of the same galaxy in different parts of the sky due to gravitational lensing, but that's a different thing which is explained another way, unrelated to the Kaleidoscope.
The Kaleidoscope is just one aspect of this speculation, but the idea of something beyond space could stand separately. How to test for those things? Good question.