In any given timeline of the DCU that is.
The JSA is the obvious answer. But how far does that go? We may be comfortable with the likes of Jay, Alan, Ted and other Golden Agers preceding Superman. But how about Power Girl? Or the rest of the Infinity Inc generation? Since that appears to be the case currently (at least as far as Power Girl goes).
Then there's Batman of course who preceded Superman in the DCAU, the DCEU, and potentially in Gunn's upcoming DCU as well - not to mention possibly in some comic-book continuities.
What about other non-powered heroes like Green Arrow?
Then there's Green Lantern. Does Hal need to get the ring and join the Corps after Superman shows up?
What about someone like, say, Blue Beetle? Based on the new film, and the possibility that its set in Gunn's DCU, it seems like Ted Kord would have preceded Superman (as would Dan Garett, but that's the case in the comics anyway)
How about Aquaman and Martian Manhunter, who I think were canonically anyway active before Superman, but kept a low profile?
Ultimately, this is where I come down on it:
JSA: Specifically all the Golden Age JSA characters. I'm also okay with Infinity Inc and Power Girl preceding Superman, provided their era is pegged as the 70's/80's...so a generation (at least) passes before Superman's debut and the sliding timescale kicking in. Oh, and Power Girl kept a low profile and wasn't remembered much, so no one compares Superman to her later on.
Green Arrow: As a non-powered vigilante, I'm pretty okay with him starting out years before Superman. Actually, this is already kind of the case, since current continuity has Green Arrow and Speedy time-traveling to the Golden Age and joining the Seven Soldiers of Victory. That said, I'm a bit iffy on the likes of Speedy (or any of the sidekicks) debuting before Superman in the 'present-day'.
Batman: Honestly, I think Batman's origin works better if Superman isn't already around. The idea of dressing up like a bat to terrorize criminals lands differently in a world where a costumed alien is already taking to the skies.
Aquaman: I'm okay with Arthur being active and maybe even getting dubbed 'Aquaman' by some of the people he encounters. But he's an urban myth (or rather, a 'marine' myth) for the most part, and Superman's debut is what makes him ready to reveal himself to the surface world publicaly.
Martian Manhunter: J'onn has canonically been on earth for decades before Superman, but he only publicaly reveals himself after Superman's debut.
Green Lantern: I'm okay with Hal getting the ring and maybe starting to train with the Corps on Oa - even going on some early missions in space, or secretely on earth. But I don't want GL as a public hero before Superman.
Wonder Woman: Well, this is current canon, and she's part of the Golden Age JSA (and perhaps the Bronze Age JSA). That said, Diana's 'modern' debut/return should happen after Superman appears.
The way I see it, Superman debuts in a world where superheroes, notably the JSA, existed back during WW2, and even up till the 70's or 80's. But its been decades since there have been any publicaly active superheroes, certainly none with his powers, so he still blows minds. However, vigilantes such as Batman and Green Arrow have been active for a few months/years in their respective cities. Aquaman has been active below the radar in the seas, and Martian Manhunter has secretely been operating for decades. Hal Jordan is possibly already training to become a Green Lantern out in space. And Wonder Woman is on Paradise Island and will soon be making her return to earth decades after her last appearance.