Superman definitely exists in the Titans universe, as revealed on the season 1 finale of the DC Universe series. For those unaware, the series is the first original live-action show for the DC Universe streaming service. It establishes its own new canon, with no relation to the Arrowverse or the movies in the DCEU. Although the show focuses on Robin, Starfire, Raven, and Beast Boy, it has included some other DC characters. Throughout the first season, however, the existence of Superman in this new universe wasn't officially established. That changed with the latest episode, which made direct reference to the Man of Steel multiple times.
In the season 1 finale, Trigon traps Dick Grayson in an alternate universe in his own mind. The apparent effort to weaken Grayson mentally places him in another reality where he's married to a pregnant Dawn Granger (Dove), and the two have a son. A previous version of Robin, Jason Todd, asks Grayson for his assistance with Batman. Todd 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." Additionally, Grayson's wife later says to him that Batman "fell out with Superman years ago." While the events in Grayson's distorted mind are from an alternate reality, such direct references to the Man of Steel prove that the superhero is flying around up there somewhere in the Titans universe.
Talking about Superman does not guarantee viewers will actually see him, however. Batman had a presence in season 1, yet the show manages to cleverly work around giving us a really good look at him. The Dark Knight is mostly shown from behind or through the use of a silhouette. It's possible that if Superman does in fact become more involved in future storylines, he'll mostly be interacting from just outside the camera's view as well. Like with Batman, it's an interesting way of involving some of the bigger names from DC, while keeping the focus on the central characters of the show.
Along with the Superman references, the addition of Superboy to the series was also confirmed in a post-credits scene. It shows Conner Kent escaping from Cadmus, which mirrors a Superboy storyline from DC comic books. In the source material, this version of Superboy is created as a clone from the real Superman. The introduction of this particular Superboy, along with multiple references to Superman himself, certainly help to prove that Superman does exist in the Titans universe. What remains to be seen, however, is if he will ever be featured in the series beyond a few name drops here and there.
As of now, the first season of Titans is available to watch in its entirety on DC Universe. Prior to the show's premiere, DC had already ordered a second season, so there's plenty to look forward to in season 2. The spin-off series Doom Patrol is also in the works, and it seems DC is hopeful this new universe will fare better with fans than the movies in the DCEU, many of which have been critical failures. For now, fans of Superman can be happy knowing the introduction of the character on Titans is, at the very least, a big possibility.