In an infinite universe, most regions lie beyond our ability to see, even using the most powerful telescopes possible. Although light travels enormously quickly, if an object is sufficiently distant, then the light it emits—even light that may have been emitted shortly after the big bang—will simply not have had sufficient time to reach us.
How dues this make any sense? If the universe originated in the Big Bang, even if it is thereafter infinite, we occupy the same relative space to the rest of the universe that we would in a finite universe. The infinite aspect really plays no role in that whatsoever. If you're talking about other light from other Bangs, that's a different question, but that isn't here this is presented.
