The Borg have been around since at least the 15th century, according to the Voyager episode Dragon's Teeth. There are suggestions in various Voyager episodes that they might be even older than that.
Yeah but as much as I like "Voyager", they loved shredding Borg continuity and rendering the initial encounter ("Q WHO"), which led to Borg interest in the humans, moot. (Or the Borg visited Earth in the 15th century, decided the humans weren't worth it, buggered off, and had no concept of how species adapt and grow over time...)