The correct evidence of universe expansion that supports the Big Bang Theory is: The temperature of the universe has cooled over time.
This cooling is a result of the expansion of the universe, as predicted by the Big Bang Theory. After the Big Bang, the universe began to expand and cool, leading to the current lower temperature compared to the early universe. This idea is also supported by the observation of the Cosmic Microwave Background Radiation, which is the remnant heat from the Big Bang that has cooled as the universe has expanded.