As far as accessibility, Gribbin isn't the best astronomy writer I've read. He seems to sacrifice clarity for conciseness, and there were many details that he seemed to breeze over so that I was confounded no matter how many times I re-read certain passages. Other details seem extraneous but are listed incessantly. For example, one of the key narratives of the book is the search for the Hubble Constant, a value given to the rate that the universe is expanding. Dozens of successive studies revised this number back and forth, and Gribbin lists the precise numbers each time it is revised, even if the change was only by a few points, the effect of which is dizzying.
On the whole, however, the implications of calculating the age of the universe as Gribbin describes are pretty mind-blowing. Just trying to comprehend the event indicated by the book's title, a beginning of time, is impossible for me. Concepts like an infinitely expanding universe, and whether the universe could snap back and collapse into itself; or what shape the universe might be---open or closed, are really interesting to think about.
Not for lack of trying, I don't feel Gribbin ever actually comes close to convincing me that astronomers have calculated a reasonable estimate for the age of the universe. For one, the final value still has a margin of error of plus or minus 1.6 billion years. And even that number was arrived to with such huge leaps of inference that what I carried away from reading the book was that the age of the universe is still very much a mystery.