How can we see photons from the big bang?

So here is what I know. In order to see light the photons have to be coming towards us and must enter our eyes (or telescopes.) Because the speed of light is constant and because galaxies move no where near the speed of light, wouldn't the photons from the big bang be heading away from us? I realize we can see very distant galaxies (and thus galaxies from a much younger time of the universe) through "look back time," but that is because the photons from that space in time are now coming in contact with where we are in space, today. How is it possible to see the photons from close to the beginning of the universe if they have all passed us by now? It doesn't make sense to me that they can be heading in our direction, since near the beginning of the universe, there would be no matter for them to bounce off of, in a different trajectory. Any explanation would be very helpful.