I'm going to skip the more philosophical part of your question. Or in other words, if you're asking, "is there any observable evidence of something outside the observable universe?" My answer is: no comment at this time.
If you're asking, "what did John C. Mather mean in talking about the edge of the universe?" I'm not John C. Mather, but here's my guess --
The curvature of the universe [1] has been computed from distortion of the Cosmic Micrwave Background and independently using other measurements.
The current consensus is that the universe is indistinguishable from a flat universe. [2]
A curved universe would have an edge, meaning there's a limit to how much could be observed. If it's x light-years until you wrap around the universe, then plant an observer into this universe at a time greater than x years and that observer (if lucky) could observe the same things in two directions by seeing "all the way around the universe."
A curved universe might lead to a "big crunch" since the curvature of space-time is caused by the quantity of matter, or not. Depends on if the matter is tightly packed enough.
A flat universe has no limit -- no matter how far in the future you plant an observer, the speed of light is not fast enough for them to observe the entire observable universe.
There's a relationship between the curvature of the universe, how dense the universe is (how densely packed the matter is), and how fast the universe is expanding (the Hubble Constant). It's likely the universe is flat, implying that the Hubble Constant is on the high end of possible values.
[1] http://background.uchicago.edu/~whu/beginners/curvature.html
[2] https://astrobites.org/2020/12/03/cosmic-clocks/