The Big Bang refers to the moment, about 13.8 billion years ago, when the observable universe began expanding from an extremely hot, dense state. It is not thought of as an explosion happening at a single point in existing space, rather, it is space itself that began expanding, carrying everything within it outward.
The evidence for it comes from several independent directions: the observed expansion of the universe today, the leftover Cosmic Microwave Background radiation, and the measured abundance of light elements like hydrogen and helium, all of which match what the Big Bang model predicts extremely well.
The Big Bang model describes how the universe evolved from that early hot state onward, it does not claim to explain what caused it or what, if anything, came before. That earlier question sits at the edge of current physics, and answering it would likely require a full theory of quantum gravity that does not yet exist.