We know that the earth is 4.5 billion years old, so the Big Bang must have happened before then. The next step is a bit more dicey. The oldest stars that are found in what are called globular clusters seem to be between 8 to 16 billion years old, so this means that the Big Bang must have happened before the oldest of these globular clusters were formed around 16 billion years ago. An independent line of investigation uses the expansion rate of the universe to estimate an age for the universe. Some estimates for the rate of expansion lead to an age near 9 billion years, while other estimates lead to an age for the universe near 15-20 billion years. In my answer to Question 1 I mentioned that astronomers are currently very baffled why the globular cluster age for the universe is not consistent with the short age for the universe which is currently favored by the observations from the Hubble Space Telescope. It should be exciting to see just how this contradiction is resolved in the next 10 years as more accurate measurements become available for measuring the expansion of the universe and globular cluster ages!