The Big Bang theory has always seemed dissatisfying to me, like there's some prima facie aspects of it that defy logic, or are "just so" in quality. It's always seemed to me to be the sort of thing that will eventually be superceded by some more complete explanation; that is, the Big Bang is correct but is part of a bigger story.
The book isn't particularly about the Big Bang (it's more about the nature of the arrow of time), but it has to deal with the subject in passing.
I can also recommend the video series The Biggest Ideas in the Universe [1]. These are a superb explanation of how modern science has arrived at the conclusions it has. You can jump ahead to the Cosmology video, if you must, but you're missing the full experience of building up an understanding that goes far beyond the usual crayon drawings the press gives us.
[1] https://www.youtube.com/playlist?list=PLrxfgDEc2NxZJcWcrxH3j...