To complete the statements regarding the discovery supporting the Big Bang theory, the appropriate terms to fill in the response areas would likely be "cosmic microwave background radiation", "cold", and "in its early stages".
So, the completed statements would read:
"Two astronomers accidentally discovered cosmic microwave background radiation, which is evidence of universe expansion that supports the Big Bang theory. This is particularly strong evidence because its temperature is cold. By observing this today, we can see what the universe looked like in its early stages."