^Depends on how you look at it.
Endgame (the Voyager finale) is what "pissed off" the Borg
The TNG Novel Resistance
is where they first start to appear and cause problems after that.
The TNG Novel Before Dishonor
is where the first really big thing occurs.
The Destiny Trilogy is the whole big event -- and likely is the more direct answer to your actual question.