If looking a distance sees that point from as it was at that point back in time then looking as far as can be, cosmic horizon, is seeing the Big Bang. The universe is expanding INTO singularity because that singularity surrounds us now

The idea that when we look far away in space we are also looking back in time is a fundamental concept in cosmology. When we observe distant galaxies, we are seeing them as they were in the past because of the finite speed of light; the light from those galaxies takes a long time to reach us. The cosmic horizon refers to the maximum distance from which light has had time to reach us since the Big Bang. In essence, it's the boundary of the observable universe. If we could somehow observe that entire boundary, we would see the universe as it was shortly after its formation. However, the statement "the universe is expanding INTO singularity" can be a bit misleading. The Big Bang is not viewed as an explosion occurring in space; rather, it marks the beginning of space and time itself. The singularity refers to a state of infinite density and temperature at the very beginning of the universe, not a point in space that the universe is expanding into. Moreover, as the universe expands, space itself is stretching, leading to galaxies moving away from each other. The fabric of space is the "arena" for the universe's expansion, and there is no center or edge that can be definitively pointed to; rather, every point in the universe can be observed to recede from every other point, leading to the common misinterpretation of "expanding into something." In summary, when we observe distant light, we are looking back in time to the early universe, but the expansion of the universe does not imply that it is expanding into a singularity. Instead, the singularity represents the beginning of all space and time.