I'm not going to list all the obvious reasons that have been listed before but real fast: they are literally the same person, old 3ER (Bran) fails to stop the NK, hops back to the past and does his best to set up Westeros (Bran the Builder) for a better shot then waits for himself in the tree. He's probably doing all that Lord of Light shit while in the tree, but that's a separate consideration. They mentioned no less than three times in the show that if you stay too long warging into the past you're stuck. There's no reason to ever mention this if it doesn't happen in the show.
New 3ER (Bran) is now giving it a shot, and if he fails he will jump back in the past and try again. This plays perfectly into this season's set ups. Why else would the NK go out of his way and risk everything to get at Bran? As long as the 3ER exists, he can never truly win. He also mentions no one has tried killing the NK with dragonfire before (drawing on the knowledge of each time they've been through this loop). Why would he even say this if he doesn't have knowledge of all the loops where they are trying to stop the NK?
Referring to the NK exposing himself to get to Bran: “He’s tried before. Many times, with many Three-eyed Ravens.” Knowing the history of Westeros and when the NK was created, we know this has to refer to different timelines.
So yes, each time the 3ER tries to stop the NK, he sets up new things to try. He probably orchestrated the whole god damn R+L situation (we saw him affecting that scene already) just to create a series of events to get the dragons here for the first time. In the same vein, this might have been the first loop where the 3ER gets marked by the NK. And if he goes back to set it up again, new Bran will take his place and not be marked yet.
There's a billion specific things from the show that point to this. I don't know why it isn't the prevailing theory, so go ahead and poke holes in it for me, please.