Question

explain how background noise detected in space provides evidence for the Big Bang Theory

Answer 1

Firstly, the left over energy in the form of microwaves provides evidence for an expansion of space. Similarly, the structure of the CMBR is uniform with minor fluctuations, this shows how galaxies may have formed as the fluctuations allowed the clumping of mass at these points, increasing gravity and in turn causing more mass to gather together. The CMBR can tell us many things about the universe but only at the point of recombination, when the universe became transparent to photons.

The Big Bang Theory perfectly predicted the CMBR. No other hypothesis can adequately explain the CMBR other than saying, "It's just there and I have no way to explain why."