That is correct. It is indeed something other than the original. Yet, it may be another exactly alike the original. Suppose I have a photo of my wife in my left pocket. I have made an exact imprint of that photo and have placed it in my right pocket. I withdraw the first photo and say to you, “Here is a photo of my wife.” Then I withdraw the one from my right pocket and say, “Here’s another photo of my wife.” You look at it and say, “That’s the same photo!” But I reply, “No it isn’t. These are two different photographs. One is in my left hand and the other in my right.” You feel that when you saw the first picture, you saw the second." And you were right. In one sense they were the same picture; in another sense they were two different pictures.
Similarly, though the only-begotten Son of God is a different divine Individual from the Father, He is exactly like his Father. If you’ve seen Him, you’ve seen the Father. They are of the same divine essence, but yet they are two distinct Individuals.
To me that explanation doesn’t seem likely. The early Christians (not only Justin Marty) saw Jesus as having pre-existed. Even as late as the fourth century after Trinitarianism became established, the original Nicene Creed referred to the Son as having been “begotten before all ages.” Even the early Trinitarians accepted that wording. But later Trinitarians realized that those words were not consistent with Trinitarian teaching. So they changed the wording of the Nicene Creed to “eternally begotten.”