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You are correct about being able to see the big bang. We are able to observe and analyze the microwave background radiation and to determine a lot about the universe's beginnings.
Also, there is a theory that if we know the exact position and velocity simultaneously of all particles in the universe we will be able to predict and see everything that has happened and everything that will happen. Because of the uncertaintity principle it is impossible to know the exact position and velocity of a given particle at the same time.
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