The band of matter is within the distance to the source of the universal microwave background, where light was first free to propagate, some 300,000 years after the Big Bang.
The source of first light is thought to be about 15 billion years times the speed of light away from us. So the band of first light, and the band of first matter is based on what we can see, not on what actually exists out there at the present time. When we look at stars and galaxies or the microwave background, we are looking back in time. The band of matter is where we look so far back in time that matter in the universe has not yet come into existense. At the present time there is no outer limit for the existense of matter. The whole universe is full of matter.
The regions of "no time" are well within the band of matter. In fact, there is astronomical evidence of at least one in the Milky Way, our own galaxy.
So here is the answer. Time does not exist in black holes in the conventional sense, according to the General Theory of Relativity. According to this theory, within the event horizon- which is the surface of a black hole within in which light cannot escape- the time coordinate, which is imaginary in that theory outside of black holes, becomes the real spatial radial coordinate of the black hole.
To be precise, this is the property of a non-rotating spherical black hole where spherical coordinates provides an algebraic solution that is accurate except near its central singularity.
This is called a canonical solution- an exact solution to an approximate geometry (since all black holes rotate somewhat and are not exactly spherical).
But nonetheles, the scientific evidence is clear that in our own backyard there is a small region where time as we know it does not exist. That's the basis of my religion. But that's another story.