What evidence supports the big bang theory?

The earliest and most direct evidence from observation of the correctness of the theory are the expansion of the universe according to Hubble's law (as indicated by the redshifts of galaxies), discovery and measurement of the cosmic microwave background and the relative abundances of light elements produced by BBN.

The Big Bang model is supported by three important observations: The expansion of the Universe as deduced from the distance-redshift relationship for galaxies and described by the Hubble law.