I'm really curious to know what The Doctor says about the creation of the universe. Does The Doctor believe in some kind of intelligent design? Did "wibbly wobbly timey wimey" thing create our universe? Or does he simply not know?
Two similar but unconnected accounts exist in classic Who. In Terminus as cited, by Jim in comments, and in Slipback (a sixth Doctor audio drama made by the BBC) in both the universe begins due to bootstap paradoxes involving ships travelling back in time to the point of the Big Bang and either (a) venting fuel into a spacial void, creating expanding space-time, or (b) impacting the Cosmic Egg* [an early illustrative view of the pre-Big Bang universe later abandoned by Physicists]. However neither of these address the issue of why there 'is something rather than nothing' ie why was there a set of preconditions or laws such that, either set of events would create space-time.
The events of The Impossible Planet/The Satan Pit strongly argue that there was something distinct from our universe before it which was different in kind (not just a cyclic iteration of similar universes*) and which had religious implications disturbing to the Doctor's essentially secular worldview.
*These exist in DW tie-in fiction but have not been expicitly stated to exist on tv, unlike parallel and alternate universes which have.
N-Space was created by a Big Bang
N-Space (or Normal Space) is the universe that the vast majority of Doctor Who is set it. Specifically it is the universe in which the Time Lords were the first species to reach the technological level that allowed them to tailor the laws of the universe to their own nature. Classic Who and some Audio Productions imply that at least one (if not two) universes came into existence before the Doctor's Universe. But that's not especially relevant to this answer.
In CW-S19E01-Castrovalva, the TARDIS travels back to Event One (also known as the Big Bang, roughly 13-14 billion BC) and we see that the Creation of N-Space is the result of a Hydrogen Inrush. It is speculated by the Fifth Doctor in CW-S20E04-Terminus that the Hydrogen is a result of a space station named Terminus that jumped back in time to before the universe and dumped its fuel. In the Audio production Slipback, a member of the High Council of Time Lords speculate to the Sixth Doctor that the Big Bang was a result of a ship called Vipod Mor gaining sentience and going back to the creation of the universe. Both of these are effectively Bootstrap Paradoxes.
The Big Bang is also reference in a backhanded manner in NW-S05E13-The Big Bang when the Eleventh Doctor triggered "Big Bang Two" via the exploding TARDIS and the Pandorica.
In short, the universe was created by a Big Bang, even if no one is quite sure what triggered Event One.
* CW - Classic Who / NW - New Who