Relative Time from a far place I have read that whenever we see the sun we are seeing the sun as it was before 8 minutes ago. Meaning if the sun were to somehow go dark we would not know until 8 minutes after. 
Now I became curious, say a civilization 4.7 billion light years away was looking at us through a very advanced telescope. Would they be seeing the Earth as it was 4.7 billion years ago (early earth formation) or would they be seeing us in our very selves right this second.  
 A: It is like mailing a letter to a friend via cargo ship. The ship takes a week to cross the ocean and deliver the letter. If your friend is just now getting the letter, he is reading about how you were a week a ago. 
It is the same with light. Light takes 4.7 billion years to travel a distance of 4.7 billion light years. The aliens would see what we were like 4.7 billion years ago. 
A: Given that the Earth formed about 4.57 billion years ago, then it is doubtful that a technological civilisation looking at us now (at the same cosmological epoch) from a "light travel distance" of 4.7 billion light years would see anything at all.
The molecular cloud from which the Sun formed, probably had a lifetime of only a few million years at most so there wouldn't be much to look at 4.7 billion years ago. 
But the general premise of what you say is correct. If you made it 4.5 billion light years away then yes, they would see a cooling new born Earth (and moon).
Alternatively, what you might be asking (awaiting clarification), is what would an observer that is 4.7 billion light years away now be seeing? This is a different question because "proper distance" is not the same as the light travel distance. This is because the universe has expanded since the light was emitted and whilst it travelled to the distant observer. The exact answer would depend on the rate of expansion and the adopted cosmological model but qualitatively, it means that the light they receive from Earth would be less than 4.7 billion years old.
A: They would see the Earth as it was 4.7 billion years ago. The light emitted by the Earth 4.7 billion years ago would take 4.7 billion years to arrive, meaning the light from long ago will hit the aliens at the present time. They wouldn't see the present day for another 4.7 billion years, because light emitted from the Earth today travels at a finite speed. It is fundamentally the exact same scenario as the sun disappearing. I hope this answered your question.
