How does Olbers' Paradox relate with the Big Bang?

Answer:
If our Universe were infinite both in size and age, then our entire sky would, by necessity, be filled with light at all times. That it is not is Olber's Paradox -- and indication that our Universe must be finite in either size or age. The Big Bang was a hypthesis that it was finite in age; and every prediction made by the BB that has been tested has supported the hypothesis.
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