In the book trilogy, Star Trek: Destiny, the Borg are first created when two injured, dying, and slightly deranged Caeliar unnaturally merged/assimilated two humans that were with them when their ship crashed in 4527 BCE as a means of survival. Humans from the 22nd century had inadvertently came across the highly advanced and xenophobic Caeliar. An accident ensued, and a few humans and Caeliar got slung back in time on the other side of the galaxy.
The newly formed Borg's devastating, insatiable appetite continued on from there until the Borg were finally taken care of in 2381 AD/Stardate 58100 (about 16 months after the events of Nemesis).
If the Earth humans are the first ones to be assimilated, why aren't they Species 001 (or 002/003 depending on how/if the Caeliar/Borg are catalogued)?