Chronologically, the earliest is 2233.04, the stardate of Nero's arrival in Star Trek (2009):
Ayel: What is the current stardate?
Captain Robau: Stardate? It's twenty-two thirty-three zero four.
Star Trek (2009)
An earlier one is referenced in the Enterprise episode "Damage", but the stardate itself is not spoken aloud:
T'Pol: I discovered a set of coordinates embedded in the document.
Archer: It's not a star system.
T'Pol: There was another embedded number. A stardate, three days from now.
Star Trek: Enterprise Season 3 Episode 19: "Damage"
Finally, although the date it references is actually later than the one from Star Trek (2009), the smallest number given as a stardate is in the first episode of Discovery:
Burnham: First Officer's Log, Stardate 1207.3. On Earth, it's May 11, 2256. A Sunday.
Star Trek: Discovery Season 1 Episode 1: "The Vulcan Hello"
Despite being a smaller number, the episode takes place about 30 years after Star Trek (2009); this is likely in reference to the stardates in the original series, which were invented willy-nilly by the episode writers.