The Big Bang is the term which refers to the origin point of the universe, an instantaneous expansion of a microscopic singularity.
Captain James T. Kirk logged that "For years scientists have theorized that if our galaxy was created from a great explosion, then the center of the galaxy might still be creating new matter." In 2269, the USS Enterprise conducted a science mission to test this theory. (TAS: "The Magicks of Megas-Tu")
The particular instant of the Big Bang was considered a "Very old hiding place" among the time traveling Q. While attempting to flee from his fellow Q, Quinn transported the USS Voyager to a point in time shortly before the Big Bang. In the few seconds before the Big Bang, the crew witnessed what appeared to be an unidentified dark oval shaped phenomena implode, followed by a large release of expanding matter, light, and baryonic particles which Quinn remarked was "perfectly normal".
B'Elanna Torres remarked that Voyager was not capable of surviving the formation of the cosmos. Q retorted by stating she should consider it an honor to have her atoms become part of the entire universe. Quinn soon transported Voyager to a Christmas tree before the newly-formed expanding universe reached the ship. (VOY: "Death Wish")
After the discovery of the Omega molecule, Starfleet cosmologists theorized that this molecule was the source of the Big Bang. (VOY: "The Omega Directive")
The Doctor referred to the Big Bang by the name of "Primordial Atom" and claimed it occurred 20 billion years ago. (VOY: "Latent Image")
Later, in 2376, an engineer aboard Voyager claimed that the Big Bang occurred 16 billion years prior. (VOY: "Good Shepherd")
The Star Trek Encyclopedia, 4th ed., vol. 1, p. 82 dated the Big Bang to approximately 13.8 billion years before the late 24th century.