Technically speaking, Steins;Gate 0 is a prequel. Even though, chronologically, it takes place after the events of the original Steins;Gate. Following the death of main heroine, Makise Kurisu, this is the timeline--or wordline--labeled “beta” in the world of Stein’s;Gate. Yet it is only because of events that take place in Stein’s;Gate 0 that the events of Stein’s Gate are possible. So, from a certain point of view, the events of Stein’s;Gate 0 are events in the future that take place before the events that already took place in the past. In the world of Stein's;Gate, time really is a flat circle.
Trying to trace that circle back to a beginning can often make things more confusing rather than clear. In theory, there is a version of the events of Stein’s;Gate 0 that follows their original course: Kurisu dies, main character Okabe Rintarou dedicates his life to fighting the future tyrannical fallout of World War III, and, presumably, when he ends up in a coma after practically getting tortured to death. However, the story that Stein’s;Gate 0 actually tells is one where the future is already trying to interfere with the past to change things. Amane Suzuha travels back in time to save the world from the dark future from World War III, rather than SERN's dystopia. From there, events occur based on the influence she tries to exert on Okabe in this world-line.
A Defeated Okabe
Interestingly, Okabe is initially resistant to her insistence that he get back into the time machine to try one more time to save Kurisu and avoid the events of World War III, after already trying and failing once before. He’s already experienced the events of Stein’s;Gate, where he tried over and over to save his childhood best friend, Shiina Mayuri, without having to change things to a world where Kurisu dies. Unfortunately, both of these world-lines exist based on "attractor fields".
In the alpha world-line, the alpha attractor field is based on the death of Mayuri, and in the beta world-line, the beta attractor field is based on the death of Makise Kurisu. Having experienced the futility of changing things so that both Kurisu and Mayuri can live, he's resigned to letting things stay as they are while he focuses more on moving past his PTSD and delightfully mad Hououin Kyouma persona and just live a normal life.
Unlike the Suzuha of the alpha world-line, who came from that SERN dystopian future, this one comes from a future where World War III would break out over an international race to be the first country to invent the time machine. Incidentally, Okabe had caught a glimpse of this Suzuha right before he sent the world’s first d-mail and shifted time enough to break it from the beta attractor field and change the world-line to the alpha one.
Yet Suzuha's goal in the alpha world-line is not to simply to change back to the beta one where Kurisu lives but to save Kurisu’s life in a way that shifts events onto an entirely new world-line where Kurisu and Mayuri are both able to live. At that point, this world-line still existed only in theory, one that had been dubbed with the, at-the-time, arbitrary name, “Stein’s;Gate”. For Kurisu's sake, Okabe had decided to give this attempt one try, despite how exhausted he already was from how much he had gone through to save Mayuri.
The Path to Stein's;Gate
However, on that first go, he failed. In fact, he inadvertently caused the death of Makise Kurisu, which begs the question if that was how things in the beta world-line went all along, which creates a time loop all its own. Either way, initially, after that failure, he’s resolved to give up on time travel altogether. Instead of slapping sense into him, as she did in the original Stein's;Gate, Mayuri accepted his decision, seeing how much pain it was causing him, and that keeps him on the path of the beta world-line and the events of Stein's;Gate 0. Hence, his hesitation to give saving Makise that second try beta world-line Suzuha keeps insisting on.
Yet it is because of what happens in Stein’s;Gate 0 that also leads to Mayuri going back in time to convince her past self to encourage Okabe to try again after all. She’s experienced how miserable Okabe is in this world-line, senses that he’s grieving a loss that, while she can't understand, she sympathizes with. Because she herself loves Okabe so much, she tries taking events into her own hands. Meanwhile, Okabe has, on a very paranoid level, forbade anyone to even think about building a time machine, even though all this time Suzuha has been pushing her future father, Daru, to do just that, in between making sure her parents still hit it off so she’s still born, Back to the Future style, and dealing with the mystery surrounding Mayuri’s future adopted daughter, Shiina Kagari.
Unfortunately, everything falls apart when Mayuri is killed by the events that kickstart World War III just as she’s getting into the time machine to go back. So now, even in this world-line, she's still ending up dead. To save Mayuri, again, Okabe ends up sling-shotted to the future of World War III that awaits them, waking up at the exact point he fell into his coma.
From there, he has to time-leap over and over until he returns to successfully send Mayuri back in time, having realized that trying to stop her won't save her. Having returned to the moment at the beginning of Stein's;Gate 0, when Okabe already failed to save Kurisu once, Mayuri can convince her past self not to let him off the hook for giving up. This unlocks a message from his future self from the Stein’s;Gate 0 future, one that gives him the answer to saving Kurisu and still keeping Mayuri alive that he hadn’t thought of the first time around. A way to finally reach the Stein’s;Gate world-line.