The universe did have a beginning...and also has an end...eternal expansion and the eventual decay of all matter into energy, leaving an absolute space.
According to the BB theory.
The universe started at a point locale with no linear dimensions and expanded rapidy, the metric expansion of space thus had a point of origin.
About 10-34 seconds after the Big Bang event the universe entered its inflationary phase whereby the univere metrically expanded it's volume by a factor of about 10 ^78
The universe's current
state had a beginning. There is no reason to suppose that the universe didn't exist before the Big Bang Event in some other state. Some physicists assert that time itself began with the BBE, but the key to this assertion is understanding its assumptions. The reason Hawking says time had a beginning is because the geodesics currently used to examine the history of the BB assume spacetime is continuous and uses discrete geodesics to describe it.
Now, what happens if we try to describe something continuous with something discrete? There gets to be a point where the discrete measuring stick stops and can't go any further. So, no wonder our current models of physics suggest a "beginning" of time, right? Discrete geodesics require that there be a zero and then a one. It's a consequence of the paradigms and the models being used, not some deeply insightful statement about the nature of reality and the universe. Furthermore, we know that the current paradigms and models (on which Hawking's assertion is based) are incomplete: we don't have a working model of quantum gravity, and Hawking's geodesics could be incomplete for any number of reasons.
His assumptions break down if:
1) Spacetime isn't continuous. As an interesting sidenote, so far three(!) independent models of quantum gravity, though themselves incomplete, suggest that spacetime may be discrete, not continuous. Loop quantum gravity, string theory, and general approaches from black hole thermodynamics ALL suggest finite, discrete spacetime. This is sort of like walking into a room with three different clocks that run on different principles that all agree on the same time -- not likely to be a coincidence.
2) Quantum gravity doesn't end up using finite geodesics.
Etc.
Also, the fact remains that time has no real ontology for itself. Space and time are like sentences; they are defined only by a collection of things in certain orders and paradigms. It makes no sense to speak of a sentence without words or just one word just as it makes no sense to speak of time without objects or with just one object.
The nature of time is also the issue here. Even if time begins, that doesn't mean the beginning of ontological existence (i.e. beginning of the universe). There are many ways in which the beginning of time wouldn't mean the beginning of existence.
1) There could be multiple dimensions of time, which is indeed the case in some string theories.
2) Time may flow in both directions from an entropic minimum. This possibility is interesting because it would mean there is another universe on the "other side" of the Big Bang timeline that, if we could see it, would be running in backwards time (and to any inhabitants of that universe,
our universe would be running in backwards time). It could even be
our universe "on the other side" such as in some cycling universe ideas.
This is also interesting because we wouldn't describe backwards time as -t. For instance, moving forward in space but backwards in time can't be typed as -v, because v = s/t (my school had us use "s" for distance), and -v would = -s/t, which would be interpreted as moving backwards in space but still forwards in time. No, to describe moving forwards in space but backwards through time we must type v
i, and similarly if just speaking of time we must type it t
i and treat backwards time on an imaginary plane. In physics there's something called CPT symmetry (or PCT, or TPC, have seen all combos) which stands for charge-parity-time symmetry. For instance the "CP mirror" of matter is called antimatter because it's reversed in charge and parity but not in time (though Feynman suggested antimatter could be reverse-time matter). The "P mirror" of levo-amino acids are dextro-amino acids, or just your reflection in a mirror. You get the idea. Well, so far we haven't discovered solid proof that there is a "T mirror," or reverse time...
...but that brings me back to why I mentioned having to type backwards time with imaginary qualifiers. As it so happens, every time we solve Schroedinger's equation to determine the wave-function for a particular thing, it gives us
two results -- a real and an imaginary answer. Scientists just throw the imaginary answer away as an artifact of the mathematics, but
some physicists are wondering whether or not the imaginary answer is telling us information about the T mirror... anyway, that's all unrelated but interesting, so I thought I'd post it.
3) There could be a more encompassing metatime. This is best described graphically, with dashes being metatime and plus signs being finite existences of what we call "time" right now:
<---------+++++++-----------+++++++-----------+++(current universe)+++------>
If metatime exists, then "time" can indeed begin and end but there is still a more encompassing metatime between finite spurts of "time."
To summarize, this isn't an easy issue in any respect, and it doesn't help that people are running around with bold (yet unjustified) assumptions.