The best way to find out if there is life on other planets is to go looking for it. This is an important motivation behind JPL's Mars Rover missions. Another way is to listen for inter-stellar radio broadcasts, like the SETI project does. A third simple and enjoyable way is just to think about it, a "mind experiment" like those Einstein used to do. We can learn a lot just by testing our mental theory. Let's try a theory that says, "We're intelligent, and we evolved after 14 billion years. Let's only look at galaxies that are 14 billion years out from the center of the universe, and their oldest stars, on the theory that they've had enough time for intelligent life to evolve." This sounds like a great concept, but on closer examination, it doesn't work at all. Here are some of the problems, and some of the wonderful scientific mysteries at play that keep scientists so busy.
1) There is no center to the universe. The Big Bang was not an explosion. It is an on-going expansion of space itself - all space is expanding. We are not "blowing out" from a center. How can space expand? You tell me and we can share the next Nobel prize!
2) Is everything in the universe essentially the same age? Not exactly. Some galaxies formed earlier, some later, but it's nothing to do with where they are relative to us or to anything else. Shock waves traveling through empty space (is that possible? yes. explicable? not really.) cause stars and galaxies to take shape over "time" (whatever that is), throughout "space" (whatever that is).
3) The oldest stars (generation 1) are bad targets for life. The area where they are doesn't contain the heavier elements needed for planet formation. These stars are in process of building the heavier elements. Better targets are newer stars, like our sun, formed from the debris of Gen 1 stars, and surrounded by the debris of their exploded remnants.
Our sun is 4 or 5 billion years old, our galaxy perhaps 10 billion. The first 5 or 6 billion years of our galaxy's life was spent burning up hydrogen and helium through nucleosynthesis to create heavier elements. See "Nobel Prize for W Fowler and F Hoyle" for the details.
4) Is Earth's span of 4 to 5 billion years the right amount of time for intelligent life? Who knows? There have been at least 6 near-total extinctions of life during that time. Are near-extinctions helpful or regressive when trying to create intelligent life? Apparently the one that nailed the dinosaurs made us (as mammals) possible.
5) Evolutionary time frame. While life on earth may have begun quickly after the planet formed, 4 billion years ago, it took 3 billion more years to build the first multi-celled creature, and another half billion to build something as complex as a fish. Presumably neither single celled animals nor primitive fish have access to radios.
6) Detectable intelligent life. A real key is "when does intelligent life become technologically capable of being detected?" Once modern humans appeared, it took 200 million years to learn how to write. For 2,800 years most of each culture's writing was burned by invading cultures. Only in the last 200 years have we been able to throw off the chains of organized theocracy and develop a culture where it is safe to freely express an original, scientific thought. Only since Marconi have we been able to communicate at any distance. Will this phase last? How long does detectable intelligent life last? What are the threats? Asteroids, thermo-nuclear war, plague, famine, climate change brought about by intelligent life are all possible limitations on the continuation of detectable intelligent life.
In conclusion, an amended version of the question might be, "How much intelligent life could exist at any point in time in our galaxy?" Make your assumptions, assign the probabilities to each, and you've got your answer! All we can say for sure is that it will be close to a second or third generation star, and won't be any special distance from the center of the universe, because the universe has no center.