They continue their voyage and begin to decipher more and more of the message that’s in the background chatter of the universe (the reason Destiny was launched). Finally, something clicks, and they’re able to decode it and discover… that it’s a message from THEM. It’s a kino video loop of fragment from the bridge of the Destiny during some sort of crisis, and it encoded into the root of the Universe.
They end up in conflict with their descendants (as noted in the ‘things we were going to do’ notes) At some point, an event takes place that forces the crew to make a decision. They can either return to Earth, or something else, but if they go to Earth, they’ll end up dooming their descendants. Now, even though they’ve been fighting it out with them, they’re STILL their descendants. Or maybe it’s some sort of imminent stellar event that threatens a planet full of descendants, anyway, they make the decision that ‘blood is thicker than water’ or something like that and use Destiny to (in some sort of super risky maneuver) dive into the event and prevent whatever will end up killing a huge number of humans.
The consequence: They end up hurled backwards in time much, much further than before and are somehow responsible for the actual creation of the universe. A kino in the bridge captures the clip that’s encoded into the background, and they end up figuring out that the Ancients had put some of this together, and that the hints they had gotten from decoding the video ended up shaping their civilization so they could make that event happen.
So the entire shebang, from Stargates to Destiny to Rings etc was all the result of a path that the Ancients started down after painstakingly decoding a video fragment of the dudes from SG:U.