The only way to see a black hole being formed 10 billion years ago is to BE 10 billion light years away, looking where the black hole is going to be. You can't look at something and see "back in time" at something else. This is the very core of the Law of Relativity. Point A looking at point B. If you're looking at something that's 1 light year away from you, you're looking at point B as it was a year ago because it took the light (or the reflection of light, as the case may be) a year to get to your position, point A. Everything is relative to where YOU are, not to what you're looking at.
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The only way to see a black hole being formed 10 billion years ago is to BE 10 billion light years away, looking where the black hole is going to be. You can't look at something and see "back in time" at something else. This is the very core of the Law of Relativity. Point A looking at point B. If you're looking at something that's 1 light year away from you, you're looking at point B as it was a year ago because it took the light (or the reflection of light, as the case may be) a year to get to your position, point A. Everything is relative to where YOU are, not to what you're looking at.