MAJOR SPOILERS for the Titans season 1 finale ahead
DC Universe's Titans season 1 finale finally confirms what was previously only hinted at - that Superman exists and interacts with the heroes of this world. The series is the first live-action TV show as part of DC Universe's slate of originals, and it's successful enough that the streaming service renewed Titans for season 2 before it even premiered. Titans isn't connected to the DCEU or Arrowverse, establishing its own world based on DC Comics superheroes - but the show never shies away from referencing the wider universe of characters. In fact, though the series largely revolves around Dick Grayson/Robin, Rachel Roth/Raven, Gar Logan/Beast Boy and Kory Anders/Starfire, Titans has introduced or referenced a whole host of other DC characters.
Hank Hall/Hawk and Dawn Granger/Dove were introduced in episode 2, then the Doom Patrol in episode 4. The second Robin after Dick Grayson, Jason Todd, appeared in episode 6, and Batman himself has been a shadow hanging over the entire first season, though he's mainly only shown from behind or in silhouette. Later in the season, Dick teams up with Donna Troy/Wonder Girl, the sidekick of Wonder Woman. But through it all, the status of Superman in the Titans universe has been a bit unclear. Dawn wore a Superman T-shirt early on, but the Man of Steel himself wasn't referenced until the Titans season 1 finale, in which he was finally confirmed to exist in this universe.
Much of the Titans season finale sees Dick trapped in an alternate reality within his mind created and manipulated by Trigon. The goal seems to be manipulating Dick until he gives into his inner darkness so that Trigon can control him, but this is achieved by showing Dick a different version of reality. In this reality, he's married to Dawn, with a son and another child on the way. But he's approached by Jason Todd and asked to help Batman. In this conversation, Jason says, "The truth is, he was never the same after you left. Alfred said it, Barbara said it, I even heard Superman say it once." Then, when Dick is discussing with Dawn whether he should go to Gotham, she says, "[Batman] fell out with Superman years ago."
Both references to the Man of Steel confirm Superman exists in the Titans world. Of course, some viewers may wonder if the superhero is only part of the reality created by Trigon, but as evidenced by everything else within the dream sequence, it seems to simply be an alternate version of reality. Meaning, all the same people exist, Trigon has simply tweaked everything to fit his needs and manipulate Dick. So Superman certainly exists, but his relationship with Batman may be different in actuality than in this dream reality.
Even if viewers aren't convinced a character mentioned in a dream reality is confirmation they exist in the real world, the Titans season 1 post-credits scene offers further proof. The post-credits scene introduces Conner Kent/Kon-El aka. Superboy breaking out of the organization called Cadmus. In the comics, this version of Superboy is a clone of Superman created by Cadmus. (Initially, this Superboy was engineered as a duplicate of Superman, though an origin introduced later in the comics made him a hybrid of human and Kryptonian DNA.) Since this version of Superboy is derived from Superman, it's further confirmation Superman must exist in Titans.
All that being said, though, it remains to be seen if Superman will ever appear in this TV universe, or if he'll simply be name-dropped. Or, with the introduction of Superboy, perhaps the Man of Steel will hang over season 2 much like Batman in season 1. While fans may be hoping to see Superman at some point down the line, it's unclear if he'll ever appear. But for now, we know Superman does exist and Superboy will be a major addition to Titans season 2.
Titans season 1 is available in its entirety on DC Universe; the series will return for season 2.