Speed of Light Just Isn’t Fast Enough

I am not a science guy. I wish I were, but my brain won’t wrap itself around numbers as easily as it wraps around words. I do have an interest in science, though, so from time to time I try to read geared-for-mass-audience science books. I’ve just started Michio Kaku’s Parallel Worlds, and a couple of chapters in I got struck by a question that I am not smart enough to see the obvious answer for:

If the light from various stars billions of years ago is just now visible because of the distance that the light has traveled, how did we get to this spot first?

My reading thus far has led me to the idea of cosmic inflation, which suggests that in the instants after the universe began there was a period of very rapid expansion, but A) I don’t know if I understand the theory yet and therefore B) I don’t know if it connects to the question I’m asking. So it looks like it’ll be back to the books on this one.