Yes, the electromagnetic waves associated with the Big Bang, known as the cosmic microwave background (CMB), have indeed been observed to be spanning the universe's space. The CMB is the remnants of the thermal radiation that was released when the universe was in its early stages, approximately 380,000 years after the Big Bang.
The CMB permeates the entire observable universe and can be detected in all directions. It consists of photons that have been traveling through space for over 13 billion years, gradually cooling down due to the expansion of the universe. These photons, initially released as high-energy gamma rays, have now redshifted to the microwave range, with an average temperature of around 2.7 Kelvin (or about -270.45 degrees Celsius).
The CMB is an important source of information about the early universe. Its properties, such as its uniformity and slight temperature fluctuations, have provided valuable insights into the structure, composition, and evolution of the universe on a large scale. Scientists have extensively studied the CMB using instruments like the Wilkinson Microwave Anisotropy Probe (WMAP) and the Planck satellite, which have provided detailed measurements of its characteristics.
In summary, the electromagnetic waves associated with the Big Bang, known as the cosmic microwave background, do span the universe's space and provide important information about the early stages of our universe.