From "Little Green Men":
Forget this timeline. The one we're going to create will be better. Once we get things in order here, we''ll contact the Ferengi homeworld and sell them our ship. The Ferengi will have warp technology centuries before humans or Klingons or even the Vulcans. We'll establish an economic empire beyond even Grand Nagus Zek's wildest dreams. And I'll control it all.
That's an interesting line. Some further dialogue for context:
NOG: No. They don't have universal translators. I recognize those uniforms from my guidebook. They're from the twentieth century.
ROM: The twentieth century? You mean we traveled back through time?
NOG: More than four hundred years.
Those are military uniforms from one of the old nation states. Australia or something.
Quark's general statement is pretty close to the dates from "First Contact". If he believes they are more than 400 years in the past in the 20th century then 1900 + 200 is pretty close (within 40 years) to 2063's first warp flight.
Based on that dialogue and "First Contact" not directly attributing the Vulcans with already having Warp drive, maybe the Vulcans at this time were using another kind of FTL drive?