No we cannot. Or at least in physics we don't believe so, simply because we have never observed an antecedent cause come before its consequent effect. If it were otherwise, a being in the future could in principle signal us and have a casual influence on our future. This is simply the same reasoning that makes us skeptical that e could ever eat the boiled eggs for breakfast before e cooked them! The other answers give you some good intuition for how a telescope fits into this reasoning.
Two comments in answer to your last paragraph: You might like to look up the notion of a Minkowski, or space time diagram. The telescope then looks along the past lightcone of the observer wielding it. So things are not as symmetrical as you seem to be thinking. Secondly, even thinking spatially without time, rather than concluding that you are at the center of the Universe from your reasoning, witness that the same thoughts (or like ones) simply argue for spatial homogeneity; any other observer in the universe would reason likewise and therefore the description of the universe cannot be affected by a shift in the coordinate origin. This is similar to observing that, for many purposes, you could shift the zero point on the number line to anywhere else, subtract the new zero point from all numbers and you'd wind up with a number line indistinguishable from the first one