It is probably very pretentious of someone with no more math than I have to aspire to explain Stephen Hawking to anyone, let alone other straight dopers, but…
… as I understand it, in A Brief History of Time, Hawking starts talking about how gravity curves things. Light, for example. Light normally moves in a completely straight line, but put some sufficiently dense object nearby and the path of light distorts around it. Nowadays we know this to be factually true. Those Hubble photos of gravitational lensing of far-distant galaxies, for one example.
Hawking says time curves like that, too.
You know what the Big Bang is all about: big expanded universe now, go back in time you also are traveling to a more dense, less spread out universe. Go back 12-15 billion years and you reach singularity and nothing “is” before that. BUT that entire sense of “go back in time”, if I understand Hawking correctly, ignores time-bending in response to gravity, which as you approach (in reverse consecutive order) the singularity you also move towards truly spectacular density and gravitatonal concentration…
From the land of equations, looking at time the way one might look at the trajectory of light that happens to pass close to a dense gravitational field but ignorant of that, one is thinking in a linear fashion. But if time curves (or umm uncurves as the density declines as the universe expands) the linear model is a misrepresentation…
Instead of thinking of, let’s say, the time frame between 13.8 and 13.0 billiion years ago as being temporally the equivalent of the time that elapsed between 1.8 and 1.0 billion years ago, we should assume the passage of time was already bent at an angle, and within that time frame was exhibiting a curve. There’s no entity to interview and ask “what was it LIKE to experience that 0.8 billion years, compared to, you know, your average 0.8 billion that go by nowadays”, and math doesn’t readily lend itself to “here is what things woulda FELT LIKE”, but I think Hawking is saying that those years back then were LONGER. And the years between 14.0 and 13.8 billion years ago (give or take; I forget exactly how old we now believe the universe to be) were even longer years, the more so as you go back in time, until very very close to the singularity what you have is a sort of infinitely timeless pre-time… a primordial “before” in which time was curved entirely away from the orientation in which we know it, gradually giving way to both physical expansion and the increase of the rate of the PASSAGE of time.
Thus, were you to hop into your HG Wells time machine and try to “go back” and see the Big Bang “event”, the “Zero Seconds and Counting” moment when the singularity goes boom, you instead get real close to that and hop again and are only marginally closer and marginally farther back in measurable time.