The Big Bang was the formation of the entire universe. About ten billion years later, our solar system, and eventually the Earth, started forming due to gravity pulling various bits of matter together. Ten billion years is a really, really long time! The two events are completely separate.
If you're interested in cosmology, there are a ton of fascinating popular science books on the topic, and research is very active and ongoing. As an introduction, I recommend Cosmos by Carl Sagan. It's a bit outdated these days, but the main points hold and it's a fascinating read from start to finish. Alternatively, if you prefer video, check out Cosmos: A Spacetime Odyssey with Neil deGrasse Tyson. It's an up-to-date retelling of Sagan's original idea.
Two generations of stars, including heavy stars that produced all the elements up to iron (including, relevant to this particular case, oxygen), and then became supernovae, which a) produced traces of heavier elements b) blew a lot of stellar material out into the universe, to become part of new star systems. So there was oxygen around by the time Earth was formed (~4.5 billion years ago, as opposed to ~14 billion for the big bang).
CRC's GED prep book used to contain this error. Most of the book was good but the "Earth Science" section looked like it had been deliberately mangled in order to discredit opponents of creationism. Or that was my theory, anyway, it was pretty bad.
http://en.wikipedia.org/wiki/Graphical_timeline_of_the_unive...