How is it possible to see the earliest and most distant galaxies?

I have seen documentaries saying we are seeing earlier and earlier galaxies closest to Big Bang. However I always wondering how this is possible considering nothing travel faster than light, and earth is not even formed yet when these galaxies are formed, so how can we see these galaxies? In other words, when these galaxies are formed, their "light" travel out and when these "lights" reaching where earth is now located in space, the problem is earth is not even formed yet! By the time earth is formed, the event (or "lights") should have long gone and we should not able to see them now. Am I missing something?