Astronomy - I don't understand it, but it's fascinating!

I read a news article the other day about some new discovery astronomers made. If you pay attention to the news like I do, you'll see these stories relatively frequently. The recently deployed Kepler telescope has been finding all sorts of new things, as are the various probes and rovers that are currently transiting the solar system or traversing the Martian terrain. That stuff is fascinating to me. I'm old enough to remember the very first Space Shuttle launch, the Hubble launch and subsequent retrofit/upgrade, and many other milestone events in the history of space exploration. But one thing that has always both intrigued and baffled me is the Big Bang. I'm not smart enough in science terms to debate or challenge it, so until some other theory comes along, I'll take it at face value. But one thing I don't understand is how the earth, our terrible, beautiful home, can be so far away from the point in space where the event actually happened. I wrote the piece below while pondering that seemingly incongruous fact. If someone out there reads this and can explain it in layman's terms, I'd be tremendously grateful.

How is this possible? Telescopes can see billions of years into the past, nearly to the time of the Big Bang. I don’t dispute that. We know how far light can travel in a year and even have a galactic unit of measurement for that - the cleverly monikered light year. What I don’t get is this. When the big bang happened, presumably all of the material in the known universe was gathered in one place, one single chunk of mass that exploded and created the universe as we know it. If that’s true, and our science instruments can see billions of light years into the past, then how did the material the earth is made from get so far away from the point in space where the big bang happened? That would mean this matter has been moving away from that point in space and time like a car driving down a highway, and presumably at the speed of light. If a telescope can peer ten billion years into the past, based on the speed of light and all that, then what we now consider our planet, the molecules that comprise it, must have been moving at the speed of light too (or faster), in order to end up so far away from the origin, right? I've read that the universe is expanding, but at what speed? Is our galaxy flying away from the Big Bang at the speed of light or faster? Here’s another way to think about it. Let’s say a ball is hit by a batter in a baseball game, the impact of the two represents the big bang. The ball is a home run; it leaves the park and lands in the seats where it stops moving. The ball represents earth at this point in time, right now as I type this. Now let’s say that the spot where the bat connected with the ball, that actual point in midair above home plate, emits light and that a fan out there in the stands next to the ball looks down on the field with a telescope or something to that spot where bat met ball. The fan can tell how far away in distance and time home plate is from where the ball is by measuring that light. So if light is the fastest moving thing known to man, and from what I know that's a true statement, then in order for the ball to be that distance from home plate, shouldn’t the ball have had to travel just as fast, or faster, than light in order to get that far away from the point of origin, from the Big Bang? Or do I just not know what the hell I’m talking about? That last one is entirely possible when it comes to this kind of stuff.