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Depends what you mean exactly by the "Big Bang". We can see the light from the when the universe first became transparent, about 370,000 years after the original event. It is conceivable that we might, some day, build devices that could see the cosmic neutrinos from when the universe was 2 second old.
But you need to understand that the universe was denser than compressed steel at that time -- there is no way that anything from before TIME = 2 seconds would have survived. No light, no particles, no neutrinos. All we can ever see is the patterns in the stuff from _after_ neutrinos started whizzing around. And right now (and for the next several centuries) all we can see the the patterns in the light from TIME = 370,000 years.
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Telescope is impliedly used to point at a spot. There is no such spot for Big Bang. Every place is at the centre of the BB and the radiation is received form all points of the sky, but not from a single spot. This is the flaw in your thinking.
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Absolutely not, that place was destroyed the instant it was created by it's own blast. But wouldn't it be grand if we could see it. There was a recent article about that very thing however and some scientists wanting to find our exact location in the universe from the exact point from the big bang, I commented that it couldn't be done and that we are only one in a million trillion galaxies that are possible and of all those, we don't even know how to prove we exist here at all except that a lot of us agree we exist.
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No.
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we don't even have telescopes that can see stars, they can only see the light no detail or even the surface, this also means the claims of discovered planets are nonsense as we obviously can't see any of those either , it's ALL guesswork and hypothesis