The Doom Patrol was originally introduced in an episode of DC Universe's Titans, but it's not immediately clear where that episode takes place compared to the timeline of the actual Doom Patrol show. Thankfully, enough context clues are given in the pilot episode for a rough guess to be made as to how the two DC Universe shows are linked.
The fourth episode of Titans was named "Doom Patrol" and introduced the characters of Robotman, Elasti-Woman, The Chief, and Negative Man into the show's reality. As the episode opened, Rachel "Raven" Roth was fleeing into the woods and discovered by Gar "Beast Boy" Logan, whom she had met in an arcade one episode earlier. Gar took Rachel back to his home - a mansion at the end of Danny Street - and introduced her to the rest of his adoptive family. Rachel stayed for dinner and agreed to let The Chief analyze her powers, which led to him being attacked by Raven's soul-self and being once more confined to a wheelchair. It was after this that the rest of the team encouraged Gar to leave with Raven and the rest of the Titans, to build a life for himself outside of Caulder Manor.
The pilot episode of Doom Patrol is all over the place chronologically, with several flashback scenes set across the later half of the Twentieth Century leading into the year 2019. It is here that Crazy Jane (Diane Guerrero) returns to Caulder Manor, having been absent for some time. It is established that she's never met Robotman, who has been living in the mansion as a coherent guest since 1995. It is suggested, however, that The Chief had been working on restoring Cliff Steele's brain for several years since his car accident in 1988 and that he only got the robot body housing Cliff's brain working properly in 1995.
In either case, no reference is made to Beast Boy in the Doom Patrol pilot, leaving it unclear just when his discovery of Raven and his leaving the mansion in Titans occurred. It seems safe to assume that the meeting occurred sometime before Crazy Jane's return in 2019, as Robotman was a long-time resident of the mansion when Raven met him in the "Doom Patrol" episode of Titans. It also seems safe to say that Gar's foster family wouldn't be as concerned about him doing what they couldn't and going out into the real world to live a normal life if they had made a trip into the nearby town before, as they do in the second half of the Doom Patrol pilot.
Given all that, the most likely explanation is that Gar Logan came to live at The Chief's mansion in 2016 (The scene depicting Gar's transformation into Beast Boy is set "two years ago" in the opening of "Doom Patrol" in Titans) and left in late 2018, just before Crazy Jane's arrival. This neatly explains away the timelines of both Titans and Doom Patrol. Now, if only there were an easy explanation for why The Chief now looks like Timothy Dalton.