Jason Bourne (Matt Damon) definitely exists in Treadstone but where is he in the Bourne spinoff series? Executive produced by Tim Kring (Heroes), Treadstone is USA Network's new action/espionage series set in the same universe as Jason Bourne. The spinoff takes place in the present day, where new Assets of the CIA's abandoned Operation Treadstone black ops program are suddenly reawakened and sent on new missions, but it's simultaneously a prequel set in 1973 that explores the origins of Treadstone.
Of course, Jason Bourne is the most famous graduate of Treadstone. In The Bourne Identity, the titular assassin was suffering from amnesia after a failed mission and he went on a quest to figure out just who he was, while the CIA mobilized Treadstone's Assets to stop their rogue agent. Set in 2002, The Bourne Identity ended with Bourne killing the head of Treadstone, Alexander Conklin (Chris Cooper), and the CIA shut down the Treadstone program, only to replace it with a similar black ops division dubbed Blackbriar. The Bourne Supremacy, set in 2004, dealt with Jason being framed for murders ordered by Blackbriar's head, Deputy Director Ward Abbott (Brian Cox), and it all wrapped up in The Bourne Ultimatum, where Bourne worked with CIA Task Force Chief Pamela Landy (Joan Allen) to expose and decommission Blackbriar. In the process, Jason Bourne learned his true name (David Webb) and how he was recruited into and trained by Treadstone to become a deadly assassin.
Jason Bourne (and Matt Damon) doesn't appear in Treadstone, nor are his present whereabouts divulged, but Bourne's prior exploits are tacitly acknowledged on the show. Bourne is referenced intermittently when CIA chief Ellen Becker (Michelle Forbes) discusses the history and decommissioning of Treadstone with her boss Dan Levine (Michael Gaston), who admitted Treadstone "is bigger than we thought". In 2004, Becker was part of the cleanup crew in New York after Bourne exposed Blackbriar in The Bourne Ultimatum but she only remembers Jason as "a rogue Asset". This suggests that knowledge of the details of Bourne's activities in New York was above Becker's pay grade back then, though she would have access to the files about Jason Bourne today. Becker's top field agent, Matt Edwards (Omar Metwally) was also in New York during the events of The Bourne Ultimatum and recalls the "rogue Asset".
An interesting inference that Treadstone makes is that while Jason Bourne is certainly famous to movie audiences, within the Bourne universe, his existence is a closely-guarded, 'need-to-know' secret. Treadstone and Blackbriar are black ops programs that were kept under wraps from most of the Agency and Bourne's war against the CIA happened over 15 years ago, with plenty of new people joining the CIA since then. It also suggests that in the years after Blackbriar was shut down, there's been a cover-up about Treadstone, Blackbriar, and Jason Bourne. Meanwhile, David Webb is only 3 years old in 1973 so he won't appear during Treadstone's prequel story.
However, Jason Bourne did resurface in 2016 and was targeted by the late CIA Director Robert Dewey (Tommy Lee Jones) as well as another Blackbriar Asset (Vincent Cassel). In Jason Bourne, Bourne worked with CIA Cyber Ops Division Head Heather Lee (Alicia Vikander) to expose Dewey's plot to use the social media platform Deep Dream as the cover for Iron Hand, a more ruthless black ops version of Blackbriar. Lee, who angled to replace Dewey as CIA Director, plotted to recruit Jason and bring him in from the cold but Bourne knew she was duplicitous and walked away. Bourne's current whereabouts are unknown but he most likely went off the grid, possibly returning to Europe, which he favors over the United States.
While the Bourne films' cocktail of blistering action and international intrigue is what Treadstone is building from, it's understandable if fans are frustrated that Jason Bourne doesn't appear on the show or is even mentioned by name. But the opening credits state that Treadstone "is based on an organization in Robert Ludlum's novels" so Treadstone is trying to expand the universe beyond Jason Bourne and hoping fans will be riveted enough by the new characters, action, and mystery to stay glued to the series, even with the Bourne absence.