Pre-universe

Before the Big Bang of the Doctor's universe, there was the "pre-universe". Various accounts give different perspectives of this state of (non-)existence.

Nothingness
The Kin remembered that the only thing that existed before the Big Bang created the universe was a particle of space and time smaller than an atom. (PROSE: Nothing O'Clock)

The Second Doctor managed to trick the Vist into travelling back before the Time Lords evolved so that they could claim ownership of time before them. They became stuck in the "no time" that existed before Event One and could never escape there. (AUDIO: The Forbidden Time) Sabbath referred to this period of "no time" as Time Zero. (PROSE: Time Zero)

When facing the Beast, the Tenth Doctor insisted that no life could have existed before the universe came into existence. The Beast mocked this belief for being baseless and emotionally-driven, more akin to religion than scientific certainty. (TV: The Satan Pit)

The Dark was said to have been formed from the remains of the void before the Big Bang. (PROSE: Fear of the Dark)

Life and existence before the Big Bang
According to one guide, there was a long lineage of universes before the Spiral Politic, known as ancestor-universes. They were so named because the creatures within them often spawned new universes (for this is how universes are made) called descendant-universes. It was difficult to make a new universe which differed too much from one's own universe, meaning that unigenetics could be traced through a lineage which had evolution over time. (PROSE: The Cosmology of the Spiral Politic)

The Kotturuh believed they had been spreading the existence of mortality in the prior universes. They did the same in the universe during the Dark Times and believed they would do so again in subsequent universes. (PROSE: The Dawn of the Kotturuh)

The Time Lords had records of "the universe before theirs" in the Matrix, which the Sixth Doctor accessed in the Matrix during his time as Lord President. He later described it to Anne Travers:

"Before this universe was created, there was another one. A totally different universe, with alien physical laws. The heavens were green, and the stars looked like... giant doughnuts, to be brutally frank. Very, very different. And, as in this universe, there were people who discovered the deeper mysteries of time and space."

- Sixth Doctor

The belief this drove at was that the Great Old Ones, powerful beings who often seemed unbound by the laws of physics and whom the Doctor faced many times, were actually surviving members of the race which had been equivalent to the Time Lords in this previous universe. (PROSE: Millennial Rites)

However, through his encounter with the Carnival Queen, the Seventh Doctor realised that most of what the modern Time Lords thought they knew about "the universe before the universe" was something stranger, being the state of reality in the Dark Times before early Time Lords managed to bind the structure of history and impose Rationality upon the universe, creating the very scientific chronology which included the Big Bang as the beginning of existence. (PROSE: Christmas on a Rational Planet)

Entropy Sirens were said to have existed before the universe. (AUDIO: The Entropy Composition)

Surviving the Big Bang
The Beast was trapped under Krop Tor by the Disciples of the Light before "light, time, space, or matter" existed, and he remained there during and after the creation of the universe. (TV: The Impossible Planet) He claimed to have inspired the Devil of all religions, including the Arkiphets, Quoldonity, Christianity, Pash Pash, New Judaism, San Klah, and the Church of the Tin Vagabond. (TV: The Satan Pit)

The entity called the Solitract existed in the primordial period where the constituting parts of the universe were swirling together and had not yet come together to actually form the universe. The Solitract was "banished" to the Solitract plane by the physical laws of the universe due to its incompatible energy constitution. Anti-zones formed when the Solitract made contact with the universe. (TV: It Takes You Away)

When the new universe was created, many powerful species from the pre-universe fled into other realities but over time found their way back. Some, like the Great Old Ones, still followed the rules of the pre-universe, giving them god-like powers. On many planets, these beings became part of the legends and religions. (PROSE: All-Consuming Fire, Millennial Rites)

The Shepherd and Shepherdess escaped the "extinction of their universe" and arrived in N-Space, where they became transparent in appearance. They moved without touching the ground and their hair and nails grew longer because they were dying in the new reality. (AUDIO: Persuasion)