The thing is - from the perspective of the unverse as it is now, the Big Bang happened everywhere all at once. You are right where it happened - but then, so is absolutely everything else as well. And all of it was packed incredibly close together* at the time. There's no "expanding ring of light" - the light started from everywhere, heading off in all possible directions, and is still going, just moving between places that were all close together at the time. Some of the light started off in your living room, and is still heading outward; but plenty of light from other places is reaching us from every direction as well.

2D analogy. Imagine the surface of a balloon. It's an incredibly small balloon when it's not inflated, but it's also incredibly stretchy. Suddenly, it starts growing - and as it does, thanks to the marvels of thought experiments, as each point of the surface starts to stretch, lots of sparkly light goes shooting off from that point in all directions along the surface. But the whole balloon is stretching, so the light is coming from everywhere, going everywhere. A couple of hours later (or maybe 14 billion years) the balloon is still getting bigger, and its whole surface is still chock full of sparkly light heading in every direction. There's no "expanding ring" - the light started out everywhere, heading everywhere.

Put back in the context of the universe, that's what we see - the Cosmic Microwave Background. Light from all over the place, that just happens to be passing here right now.

*"Incredibly close together" is as far back as we can go. There's a point where everything is so close together that our current models of the way the universe works simply break down. What happens before that is, basically, currently unknowable.