The evidence that supports the idea that Cosmic Microwave Background (CMB) radiation is a remnant of the Big Bang is: Its temperature is uniform.
The CMB has been measured to have a nearly uniform temperature across the sky, which is consistent with the predictions of the Big Bang theory and indicates that it is a remnant from the early hot and dense state of the universe. Additionally, slight fluctuations in temperature (not great fluctuations) are observed, which provide information about the early universe's density variations.