I guess theoretically if we could go faster than light, which we clearly cannot, at some point we'd be able to see the big bang itself. Just curious - how far away is that light?
The particle horizon is the point where light arriving at us now would've had to have been emitted at the big bang (though note this is hypothetical as the Universe did not become transparent to light until it was several 100,000 years old).. How far away it is depend on the model you use (not to mention there are several different distance measures in cosmology), but it's proper distance is reckoned to be about 46.9 billion light years.
A note of caution though, when calculating the particle horizon cosmic inflation is usually ignored. What is light arriving (again hypothetically) from usually called the particle horizon therefore would be actually light that was emitted from just the end of the inflationary epoch. If you were to take a model with a big bang singularity and inflation the "true particle horizon" would in fact be much further away.
I guess theoretically if we could go faster than light, which we clearly cannot, at some point we'd be able to see the big bang itself.
If we travel instantaneously across the universe (as measured by cosmological time), then no, theoretically that's not the case. Our theoretical assumptions involve large-scale homogeneity and isotropy, meaning that the view different observers is basically the same regardless of where they are, at least at the same cosmological epoch. This is called the cosmological principle.
Mind, because of the way relativity works, an FTL drive might also be capable of taking you back in time, so perhaps you could theoretically see the Big Bang after all. But that's obviously more to do with time travel than going to distant places.
Seems like the moment something happened, light was dispatched and unless particles traveled faster than the speed of light to obstruct that light, if I were to appear in front of that light, for a single tiny moment, I'd see that little white dot that would've appeared the moment the big bang began (and then see everything that happened afterward). Why not? Light point A -> same light at point B [observer]. Where's the complication?
You seem to have an implicit assumption about where the Big Bang occurred. It actually occurred everywhere. Including here. See this question.
Imagine looking out to the most distant galaxy that you can barely see. Because of the finite speed of light, you are looking at it not as it is, but as it was in the distant past. You are just now catching light from that distant place.
If you were instantly transported to that place, and look back to where the Milky Way should be, you won't see it, but rather as this area of space was in the distant past. You'll be just catching light from somewhere the Milky Way area.
In other words, you will see light from the distant past no matter where you go. Because the Big Bang happened everywhere, light from it (well, actually from recombination epoch later, because the universe wasn't transparent before then) is present everywhere. And hence it'll look about the same no matter where you go, again assuming isotropy and homogeneity.
Seeing (or not) the "light from the big bang" has little to do with how fast we can travel.
The cosmic microwave background is here and now; you can pick it up as short wave radio interference. This light was emitted when the universe had cooled to about 3000 degrees, some 400,000 years after the big bang.
The problem is that before that time the Universe was opaque to radiation. That is, light that was emitted was quickly reabsorbed or scattered before it could travel very far. If that were not the case then we would be able to see light from an even earlier epoch. It would be red shifted because of the expansion of the universe by factors of well over a thousand.
In fact there is (or is predicted to be) "radiation" all around us from the first second after the big bang, in the form of low energy neutrinos. Neutrinos interact extremely weakly, so the universe became transparent to them at much higher densities than it did for light. These particles have been travelling the universe since, in all directions, gradually losing energy to the expanding space. Efforts are underway to detect these neutrinos, which would be a superb vindication of the big bang model.
There is no "far enough away" to see the big bang. The bang was the creation of space and time, so every view within the universe is a view from inside the bang. To see it from outside, you'd have to view the bang from whatever space the universe is embedded in; assuming it is embedded in a higher space, and that space has something like a time-axis. The 3.7°K microwave background photons hitting us right here, right now is the best view of the consequences of the bang that we'll ever get; barring exotic SF scenarios of course.
the light from the big bang is in your living room... because that is where the big bang took place... did you know you were so special? Just kidding, but maybe I misunderstood your question. I think what you are asking is, well if you look into deep space you are looking back in time since it takes light X amount of years to travel to the observer. So look far enough back and you would see the big bang right? We already thought of it, and the problem is you can't see the moment of the big bang, because there were no such thing as photon's at that moment. It took about 400,000 years (an afternoon nap on the scale of the universe) for the intensity of the moment of creation to simmer down enough atoms could form removing the opacity of the universe freeing photons to begin their cosmic journeys.. If you were to look out that far you would just see a big opaque blob like trying to look into the center of the sun. The light from that moment still exists and you do see it... you just don't SEE it. The spectrum of the sun's light that has the highest intensity is in the visible light wavelength. One would imagine that all species of the universe see in the same wavelength and thus we would all agree on what visible light is. This is not true. We see in the visible wavelengths because of evolution. Our eyes adapted to the highest intensity light available. Think about natural selection. Ancient primates who could see better would be better hunters. So those who were utilizing the highest intensity light the best would be ideal mating candidates giving birth to more off spring with eyes like there own (a little theory of mine). If you grew up on a planet with a sun that gave off a lot of infrared light you would see in infrared. Anyway, what I am getting at is if we somehow managed to evolve to this point on a rock with no companion star (an impossibility for all intents and purposes) in some dark corner of the universe where there was no other really intense light around, theoretically eyes would have evolved to see in the cosmic microwave background because it would be the only light available. CMB radiation (the afterglow of the big bang) is ubiquitous. It is everywhere at once. It gets cooler as time goes on as space time stretches, stretching the wave length of the light making it harder and harder to detect. I hope that answered your question.