I might not have been clear in my idea. Apologies for the confusion. Let me see if I can clarify.
What I mean by the Borg having all their knowledge going back in time is they already have the technology from the 24th century Federation, too. They have assimilated lots of Starfleet officers and ships, so they already have the technology either in the sphere or by using the collected knowledge, which they can rebuild whatever technology they need.
Plus, given Data's population count of the altered Earth, I don't think there are fewer overall people in the past. (Though admittedly, it's more likely to be fewer than the 24th century.) Without the Federation in the way, the Borg can have the entire Alpha Quadrant, and likely a good chunk of the Beta Quadrant and possibly have started on the Gamma Quadrant (assuming they know about the Bajoran wormhole), assimilated by the time FIRST CONTACT begins. Then reconnect with the Delra Quadrant Borg. Their goal of assimilating the entire galaxy happens centuries before it was meant to.