I’d argue the opposite. Most religions don’t care about aliens existing or not (ancestor worship, Shinto, all Dharmic religions as far as I know, animism, etc.). Others have already made arguments why aliens should exist according to their religion (argued by at least one catholic “saint”), while others would find it difficult but not impossible to fit aliens into their belief systems.

Similarly, the Big Bang at best disproves the literal nature of a religion’s creation myth, if such a myth exists to begin with. An ancient Greek would just tell you that obviously the Big Bang or its aftermath is Chaos, from which the first gods came. An elf in Tolkien’s legendarium would tell you that obviously that was the beginning of Ea (the universe), sung into existence by the first notes sung by the Maiar. A Hindu might say something about Brahman being split into smaller existences.