Personally, I don't believe in creationism but I've got some issues with the astrophysical explanation that, essentially, there was nothing and then it exploded. The origin of life seems very unlikely, if not impossible, but I can't say that I know enough to say it is or is not impossible. Life, I thinkt, is so ridonculous that I wouldn't say it couldn't randomly appear and then proliferate.
Actually, there are other ways of dating much older inorganic objects, such as Uranium-Lead dating, which is generally quite precise and relies on species of rock rather than organic material. Different methods of radiometric dating are used for different periods of time, depending on the half-life of the isotope. The time period can range from a couple thousand years to several billion years (Rubidium-Strontium dating could be used to date samples older than 50 billion years).