The Big Bang theory is supported by three main pieces of evidence: the expansion of the universe, the cosmic microwave background radiation, and the abundance of light elements.
1. Expansion of the Universe:

Redshift:
Galaxies are observed to be moving away from each other, and the farther away they are, the faster they are receding. This redshift of light from distant galaxies is a key piece of evidence.

Hubble's Law:
Edwin Hubble discovered a relationship between a galaxy's distance and its speed, confirming that the universe is expanding.
Uniform Expansion:
The expansion is uniform, meaning that it's happening in all directions from a common point.

2. Cosmic Microwave Background Radiation (CMB):

Afterglow of the Big Bang: The CMB is a faint radiation that fills the universe and is considered the afterglow of the Big Bang.

Temperature Matches Predictions: The CMB's temperature and characteristics strongly match the predictions of the Big Bang theory.
Observed by Telescopes: The CMB has been observed and measured using telescopes.

3. Abundance of Light Elements:

Big Bang Nucleosynthesis:
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The Big Bang theory predicts the relative abundances of light elements like hydrogen, helium, and lithium.
Observations Match Predictions:
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Observations of the universe's composition match the predicted abundances of these elements.

This video explains what is the evidence for the Big Bang: