Final answer:
The Big Bang theory is supported by the observation of cosmological redshifts of galaxies indicating the expansion of the universe and the detection of cosmic microwave background radiation, which is the cooled remnant of the initial explosion.
Step-by-step explanation:
Two key pieces of evidence that support the Big Bang theory are the cosmological redshifts of galaxies and the cosmic microwave background radiation (CMBR).
The first piece of evidence is the observation that galaxies are moving away from each other, with a speed proportional to their distance. This is indicated by the redshift of the light coming from those galaxies. A redshift means that the light is stretched to longer wavelengths, which can be interpreted as the galaxy moving away from us. This expansion of the universe is consistent with what we would expect from a Big Bang event.
The second key evidence is the cosmic microwave background radiation. This radiation is a relic of the early universe, predicted by the Big Bang model, and has been detected as a perfect blackbody spectrum corresponding to a temperature of 2.725 K. This uniform radiation pervades the universe and is thought to be the cooled remnant of the initial explosion.