James Gatz created Jay Gatsby in order to remake himself into a rich socialite, something he believed would increase his chances of winning Daisy back. It was James Gatz who had that initial relationship with Daisy. Gatsby wants to recapture that feeling and that relationship but with this new persona (as he believes this is the best way to do so). So, Jay Gatsby is both a continuation and a negation of James Gatz. Gatsby is therefore supported by and suppressed by the past. Gatsby pushes on into the future to recreate some old dream, or as Fitzgerald puts it in the final line, "So we beat on, boats against the current, borne back ceaselessly into the past."
In Chapter 6, people are beginning to wonder more about Gatsby's past as it becomes clear that nobody really knows him. Gatsby is known for being an accommodating host at his parties, but he is equally known for being mysteriously aloof. It is in this chapter that Nick chooses to give Gatsby's background. Gatsby tells Nick of his plans to win Daisy back and Nick says, "You can't repeat the past." Gatsby, naively and romantically says, "Why of course you can!" Nick realizes again that Gatsby is attempting a fantastic paradox: remaking himself into something new but repeating something from the past:
He talked a lot about the past and I gathered that he wanted to recover something, some idea of himself perhaps, that had gone into loving Daisy. His life had been confused and disordered since then, but if he could once return to a certain starting place and go over it all slowly, he could find out what that thing was. (Chapter 6)
One of the things that makes Gatsby so interesting is his conflation of time. In a sense, he lived non-linearly but that was only a consequence of his romantic idealism. He longed for this dream (Daisy) which was from his past. He pushed on into the future in order to re-achieve this dream. He was quite literally trying to merge the past and the future together.
Gatsby believed in the green light, the orgastic future that year by year recedes before us. It eluded us then, but that’s no matter—tomorrow we will run faster, stretch out our arms farther . . . (Chapter 9)
The green light represents Daisy, which represents the past for Gatsby. Yet, in trying to recapture the past, he runs ever faster into the future.