In one of the concluding episodes of Star Trek Discovery's first season, we saw Michael Burnham saying to Emperor Georgiou that her empire extends to every system in her Universe's galaxy. We can conclude that Emperor Georgiou has defeated the Borg in her universe. The Emperor would know the presence of the Borg by going through the Defiant's data core. So how did she do it?
Emperor Georgiou mentioned that the Klingons are like a virus that need to be terminated at their source. The words used by her strikes similarities with the Borg being like a virus themselves. We can assume that she has used the same tactics for the Klingons on the Borg as well.
The emperor could have commissioned the building of several charon type ships. Scout ships with Spore drive would firstly be deployed to locate the Borg's Nexus at Unimatrix 01. A lone ship would be sent to its doorstep to be assimilated by the Borg, and it would carry a virus long enough to bring chaos to order. Because this is the time before the Borg Queen encountered Janeway's tactics, the Borg would not be prepared for a virus attack.
After the Borg has been infected with the virus and crippled, the fleet of Charon type ships would be instructed to jump to unimatrix 01 and destroy the Borg's unicomplex. The charon type ships are capable of destroying single Borg cubes with a single Spore-powered missile. The fleet would then move on to bombard all Borg planets and destroy all of their ships and bases within Borg space in a very short time.