A telescope would see the image at the same time as you did with the naked eye - only bigger, or clearer. A telescope doesn't change the time of the image being viewed. The Big Bang is different because in a weird and twisted sense it sort of happened everywhere, and everyquote[when], at once. So there's no fixed time when you can look back and say "Oh, look, there goes the Big Bang - and, it's gone". The analogy is closer to thinking of the Big Bang as a picture we are walking away from. No matter how far away we are, the picture stays in the same place with the same image. The analogy isn't perfect but it's not a "blink at you missed it" thing.