What I mean is more literal. Like, take our current computers. Run as long as they like, with as complex of algorithms as you can imagine, and no computer will ever think of a 2.
Solve the best order of slicing the bread and meat and lettuce, which order to mayonnaise the bread and stack the filling, and a computer will astonish us in what order it does thing in to make a sandwhich efficiently.
If you ever look into great inventors, they all describe a moment of clarity where they saw a thing that didn't exist. The greeks called these muses. And, they are literally outside the box events. There is no amount of churning inside the box that would ever get us some of the things we have now.
As far as we know. :) I try not to say never, or always. No way for me to prove such things.
This is something I know, but it is also something I cannot prove.
You see, my life has been one of getting outside my boxes... only to find myself in a bigger box. Analysing my thinking before and after, I have realized that there is no amount of thinking that would get one outside the box. The "epiphany" as you have said, came from outside.
Also, the universe is a box. There are thoughts that we cannot think. But, I cannot describe them, I cannot quantify them, I cannot tell anyone else of them. There is no proof that I could ever give. Because, to do so, I would have to change the universe to include that thing/thought. And, once I did that, the universe would become bigger... and the proof would poof.
And I believe the term you are describing is "epiphany". Would this be accurate? I have experienced such moments myself.