The “Big Bang” theory was proposed by a Catholic Priest. And many Catholic Christians today are not young earthers. The Catholic Church does not have a definitive teaching on this, and thus a faithful Christian is free to believe either.
As far as evolution goes, a Catholic must believe that men were created by God and did not evolve from animals. We do know that animals (and you could argue human beings too) have evolved over time to adapt to their environment. And through breeding, also have changed a bit over long periods of time.
Personally, this is not a deal-breaker. My Faith does not hinge on whether the Earth was created in 7 literal, 24-hour days or over a billion years, it doesn’t change the fact that God created. It doesn’t make the Bible any less true either.
Going back to the big bang theory, every time a human being is, and at the moment, conceived, is kind of like a mini big bang theory. There is a spark when life occurs and where the soul and the incarnate are infused. How amazing is this?!