The ability to "see" light or radiation from the early universe despite the limitation that matter cannot travel faster than light is due to the expansion of the universe and the concept of cosmic light travel time.
In the early universe, the universe was much smaller and denser. As the universe expanded, it also stretched the wavelengths of light within it. This stretching is known as cosmological redshift. As a result, light that was originally emitted in the early universe has been stretched to longer wavelengths, shifting it towards the red end of the electromagnetic spectrum.
The expansion of the universe also leads to another crucial factor: cosmic light travel time. The speed of light is finite, so light from distant objects takes time to reach us. When we observe distant objects in the universe, we are effectively observing them as they were in the past. The farther away an object is, the longer it takes for its light to reach us.
In the case of observing the early universe, we can look back in time by observing the most distant objects and the oldest light. The cosmic microwave background (CMB) radiation, for example, is the faint afterglow of the Big Bang and is the oldest light that we can observe. It originated about 380,000 years after the Big Bang when the universe had cooled enough for atoms to form and photons to travel freely.
By studying the CMB radiation and other forms of light from the early universe, scientists can gain insights into the early stages of the universe's evolution, such as the formation of galaxies, the distribution of matter, and the conditions shortly after the Big Bang.
In summary, while matter cannot travel faster than light, the expansion of the universe allows us to observe light that was emitted in the early universe. By looking at distant objects and measuring the cosmic light travel time, we can study the early stages of the universe's history.