I posit that a big, global, perfect miracle in our real world has to be divine in origin.
Any imperfections in miracles discount them from being caused by an omnipotent god. So as magical superpowers don't exist (outside of religion, anyway) then we can critically judge a putative big, global miracle on the basis of either:
a) if it's perfect, it's divine, therefore it's a real miracle, or
b) if it's imperfect, it's not divine and so it's not miraculous.
We can discount the possibility of c) it's perfect, but it was done by magical aliens. Because magic doesn't exist (outside of religion, anyway).
So god could make his presence known, unambiguously, by performing a big enough miracle. But he doesn't. It's almost as if he doesn't care if we get to spend eternity in his presence...
To take your example of the Matrix then from the point of view of the inhabitants of the Matrix, the agents were effectively godlike. Or demonic, depending on your point of view. They were able to move in and out of the (computer-generated) "reality" at will, they could change "reality" to suit their purposes and they could choose to ignore physical laws whenever they liked. Of course, the movie itself plays very clumsily heavily on just this concept.