Question

What specific evidence supports the big bang theory?.

Answer 1

Evidence doesn't support theories.

A theory is an explanation that's offered to support evidence.

The big bang theory is a proposed mechanism that can explain the observed abundance of the natural elements, the observed distribution of the cosmic microwave background, and the observed expansion of the universe (which itself is a theory that can explain the observed red shift of the light from distant galaxies).

Answer 2

the measured abundances of elements, the observed expansion of space, and the discovery of the cosmic microwave background (CMB). The CMB refers to the uniform distribution of radiation that pervades the entire universe.