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.