Event One

Event One, also known as the Big Bang, was an explosion, the biggest "in history" according to Nyssa (TV: Castrovalva) and the biggest "of all time" according to Fifth Doctor, (TV: Terminus) which resulted in the creation of the universe. (TV: The Big Bang) The Beast called it "the Cataclysm". (TV: The Satan Pit)

Pre-universe
At least one universe existed before the one the Doctor lived in. (PROSE: The Pit, PROSE: Millennial Rites, TV: Secrets of the Stars) The Great Old Ones, the Beast, and the Disciples of the Light, natives of this pre-universe, survived the Big Bang. (PROSE: The Quantum Archangel, TV: The Impossible Planet) The Ancient Lights continued some sort of existence after Event One, but was unable to enter the new universe. (TV: Secrets of the Stars)

Before the universe, two beings of good and evil, possibly related to the Great Old Ones, existed and were caught in the explosion. While it is unclear what happened to the good force, the evil force, which later came to be called Fenric, survived and encountered the Doctor in 3rd century Constantinople and in Maiden's Point in 1943. (TV: The Curse of Fenric)

The Second Doctor tricked the Vist into travelling back in time to before the Time Lords evolved so they could claim ownership of time. Instead, they travelled to a point before the Big Bang, where there was no time for them to move across, and were thus trapped there forever. (AUDIO: The Forbidden Time)

The Eleventh Doctor tricked the Kin into thinking he was taking it to the Dawn of Time. Instead, he took the Kin to the moment just before the Big Bang and left it there, in the Void before Creation, where it could do no harm to the universe. Its last word before the Doctor left was, "Doctor!" (PROSE: Nothing O'Clock)

The Doctor's universe
During the first period, there was an "empty void", (TV: Terminus) then matter exploded outward in the form of hydrogen. (TV: Castrovalva)

The Doctor speculated that the massive ship Terminus had time-jumped at some point, discharged its fuel and instigated the Big Bang before time-jumping a second time back from the distant past. (TV: Terminus)

Another account had a Time Lord from the High Council stating to the Sixth Doctor that the Vipod Mor, headed back in time to the creation of a galaxy, overshot and travelled back to before the universe, thus causing the Big Bang as a "dense monoblock of matter". (AUDIO: Slipback)

The Leptonic Era followed the Big Bang. (TV: Time and the Rani)

The Big Bang Two
The universe in which the Doctor's adventures took place was destroyed when the TARDIS exploded. The Doctor created a new big bang which rebooted the universe. (TV: The Big Bang)

References to the Big Bang
A Time Lord told the Doctor that the Time Lords had mastered transmat technology when "the universe was half its present size". (TV: Genesis of the Daleks)

According to the Seventh Doctor, the creation of the universe occurred 13,500,020,012 years before a specific date in the early 22nd century, when he decided to celebrate it. (PROSE: Transit)

The Fourth Doctor implied that he had watched it happen, or at least that other sentient beings had done so. (TV: Destiny of the Daleks)

The delusional Monarch, believing himself God, wished his ship to travel back to the beginning of the universe and witness himself creating it. (TV: Four to Doomsday)

A Vess weapons factory was set in a pocket dimension sustained with energy drawn from the Big Bang. (AUDIO: The Light at the End)

According to the Eleventh Doctor, the Eye of Time was believed by some to be the left-over core of the Big Bang. (GAME: City of the Daleks)

When asked "what happened", the Twelfth Doctor referred to the Big Bang, dinosaurs and bipeds. (TV: The Girl Who Died)