Event One

Event One or the Big Bang referred to the creation of the Universe and the beginning of all ages.

Pre-universe
At least one universe existed before the one the Doctor lived in. (NA: The Pit, MA: Millennial Rites, SJA: Secrets of the Stars) The Great Old Ones and the Beast existed and were able to survive the Big Bang, though the Great Old Ones gained advanced powers in the process. (PDA: The Quantum Archangel, DW: The Satan Pit) The energy entity known as the Ancient Lights continued some sort of existence after Event One, but was unable to enter that new universe. (SJA: 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 exploding new universe. 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. (DW: The Curse of Fenric)

The Doctor's Universe
During the first period, there was an "empty void", (DW: Terminus) then matter exploded outward in the form of hydrogen. (DW: 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. (DW: Terminus)
 * These two descriptions may be of the same event. Hydrogen was an excellent fuel for fusion, and may be the fuel dumped by Terminus. If Terminus did cause Event One, then the entire universe was a predestination paradox.

The Leptonic Era would follow. (DW: Time and the Rani)

Contradicting this, a Time Lord from the High Council stated to the Sixth Doctor that the Vipod Mor, headed back in time to the creation of a galaxy, would overshoot and travel back to before the universe, thus causing the Big Bang as a "dense monoblock of matter". (BBCR: Slipback)
 * These two reasons may both have been true, with the fuel of Terminus colliding with the Vipod Mor.

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. (DW: 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". (DW: Genesis of the Daleks)
 * The Time Lord said this to the Doctor on Skaro at an indefinite moment near the end of the Thousand Year War, which happened at, the very latest, before the year 2157, by which time the Daleks already had interstellar spaceflight.


 * According to the Seventh Doctor, the creation of the universe occured 13,500,020,012 years before a specific date in the early 22nd century, when he decided to celebrate it. (NA: Transit)
 * We do not know if he counted the date in Earth or Gallifreyan years.


 * The Doctor implied that he had watched it happen, or at least that other sentient beings had done so. (DW: Destiny of the Daleks)
 * The delusional Monarch, believing himself God, wished his ship to travel back to the Big Bang and witness himself creating the universe. (DW: Four to Doomsday)