The Big Bang proper, as opposed to issues of inflationary cosmology, anisotropy, etc., is absolutely compatible with Genesis 1:1-4 or so, the only part of the Bible which directly addresses it. At the instant of the Big Bang, the universe was extremely small, extremely dense, and of an extremely high temperature – on the order of six billion degrees (at this point and with that generality, the temperature scale used makes no effective difference). The only particle which can exist at six billion degrees is the photon (along with the neutrino and hypothetically the graviton, issues not relevant).
Yom, the noun describing what God worked during six of in Genesis 1, is translated “day,” but like English “day,” has the three meanings of “period from sunrise to sundown,” “period between a given time of day (midnight, sunset, noon, etc.) and the recurrence of said time of day,” and “indefinite period of time during which someone or something flourished,” as in “In Abraham’s day…”
But as suggested elsewhere, understanding Genesis 1 as story makes sense both in terms of writing style and in terms of divine intent. If God had wanted to provide scientific treatises, He would have called Democritus, not Abraham, and Aristotle, not Moses. What He’s intent on conveying is that (1) He did it all, not some demiurge or deus otiosus, (2) He did it by His Word calling things into existence (cf. John 1:1-18), (3) He did it in an orderly sequence, not all at once, (4) He made human beings an integral part of His creation, (5) He called everything He created good, and (6) He made a time of rest, refreshment, and union with Him an integral part of His creation. Thrown into the mix are snide comments constrasting the Israelite creation story with the Babylonian and Ugaritic creation stories: their creators work with chaos; He creates the chaos and then shapes it; Marduk wrestles with Tiamat, the monster of the deep; He creates the monsters of the deep; Ea creates and then chills out, leaving the running of the world to his offspring; He not only creates but takes an active interest in His creation and His creatures.
And the whole thing is told in a memorable repetitive style: “On the nth day God said, ‘Let there be X.’ And X came into existence, with appropriate details for X. And God saw that it was good. And the evening and the morning were the nth day.” I’ve read that “evening” and “morning” need not be literal, any more than “day” is, to conform to the Hebrew terminology: they’re words for “downfalling” and “uprising,” not the specific English terms that mean only particular times of day. But without better knowledge of Hebrew than I have, I cannot confirm that as accurate.
However, that formula is reminiscent of children’s stories. Take Goldilocks and the Three Bears, for example. Any three-year-old will tell you with glee that Poppa Bear’s whatever is bad one way, Momma Bear’s same thing is bad the opposite way, and the same object for Baby Bear is just right. That repetitiveness makes for a memorable story that carries a point.
Likewise, the master prose craftsman who put together the Genesis story made sure that people of whatever age or literacy level would be able to grasp the points he was making by the same formulaic repetitiveness, bringing home the message that God made everything, made it intrinsically good, that the same God who created it all is the one who is involved with the individual person…
For the Bible-literalist, the idea that there are other meanings to “truth” than literal narrative account is difficult. Often he is best able to grasp it by looking at Jesus’s parables – which contain subtle and important truths clad in fictional anecdote.
But, for me at least, the idea that God in some way inspired Scripture is important – it’s not the manufactured ravings of a bunch of desert nomads, but their best understanding of who He is and what He is like – evolving over time. Just as a small child is unable to grasp parental guidance as opposed to discipline, and therefore needs to be told what not to do, while an older child or teen may be guided to make wise decisions for him/herself, so the concept of God evolved from absolute potentate to loving Father. (Note carefully that that says nothing about the nature of God, but about human concepts regarding Him.)