Disco Elysium's Steam store page (opens in new tab) still lists its release date as "to be announced" but developer ZA/UM just reposted an article that cites the more optimistic time frame "the end of the year."
The feature was originally published on May 1st in French on Canard PC (opens in new tab). Today, ZA/UM posted an English translation to their Steam news feed. Although the majority of the article cites details about the grim detective RPG that we already know (amusing dialogue and skills that manifest as voices in your characters head), there is a very quick mention of Disco Elysium's release.
As one commenter aptly quips with a "tl,dr," this best bit of information is buried in the last lines: "if Disco Elysium does well after its release at the end of the year..."
Although one comment in one interview is not much to go on, and indie games often launch later than their initially announced release dates, the fact that ZA/UM chose to post the translated article without any caveat or correction suggests that the end of 2019 is a likely release window. This is definitely a clue that we were meant to find. Or else I'm just as bad a detective as Disco Elysium's hungover and washed up protagonist.