You can blame my mom for this one. We bought a ton of vinegar because we're having a stray cat problem and trying to drive them away from the place without too much harm, and apparently vinegar is a good cat repellent.
But that aside, when is the first evidence of vinegar ever being made?
Vinegar is created by acetobacter, a kind of bacteria that is naturally occurring- notably, occurring in the guts of fruit flies. When yeast ( a fungi) encounter sugar, they will start to ferment it into alcohol. If acetobacter bacteria are present ( and, of course, that can occur because fruit flies are going to be drawn to the smell of fruit juice) and conditions are right, they will begin to ferment the alcohol to acetic acid.
Whenever wine, beer, hard cider etc are made, there is a chance that it will be turned into vinegar accidentally. But if , say, a farmer had vinegar in a barrel, adding wine or cider to it would result in more vinegar being produced.
So, essentially, your question is , how long have people done fermentation, made beer or wine? That's going back to at least 7,000 BC , for China.