The Big Bang was not an explosion in space; rather, it was the rapid expansion of space itself. It is important to note that the concept of "space" as we understand it today did not exist before the Big Bang. As the universe expanded, space itself stretched and continues to expand.
In the early stages of the universe, immediately after the Big Bang, the universe was extremely hot and dense. During this time, the universe was filled with a plasma consisting of charged particles, such as protons and electrons. These charged particles interacted with photons (electromagnetic waves) through scattering and absorption, making the early universe opaque to light.
As the universe expanded and cooled down, about 380,000 years after the Big Bang, the plasma began to recombine, forming neutral atoms. This event, known as recombination, allowed photons to travel freely without being constantly scattered. These photons are the ones we observe today as the cosmic microwave background (CMB) radiation, which permeates the entire universe.
The cosmic microwave background radiation is not confined to a specific region of space; it is spread uniformly across the entire observable universe. Since the speed of light is the fastest known speed, the cosmic microwave background radiation has had sufficient time since its emission to reach us from all directions, spanning the vast distances of the expanding universe.
In summary, while the expansion of space itself has allowed the cosmic microwave background radiation to propagate throughout the universe, it is not accurate to say that these electromagnetic waves are actively spanning the universe's space. They are remnants of the early stages of the universe that have traveled through space and time to reach us.