When Picard encounters the Borg in the Delta Quadrant for the first time, after that the Federation starts making some preparations in case they attack. If they knew of the Borg already, there wouldn't probably have been any sort of reaction to that effect.
Enterprise is indeed a tricky factor in this. The Federation should have had rudimentary knowledge of the Borg by the time Picard ran into them due to the events depicted in Enterprise.
However, I see no reason why Enterprise would take place in NuTrek (what a retarded term, anyway), since if it did, it would probably been told so by the people in charge. If we want to leap into conclusions, we could just as well say that since Picard and the Borg went back in time in First Contact, leading to an encounter with the Borg that early in the timeline, and then leading to the events of Enterprise, the events in "Q, Who?" never actually even took place because the future was changed.
I was personally under the impression that the NuTrek universe was essentially identical to the prime universe before the black hole through which Spock and Nero got tossed there, or didn't even exist and was only created as a result of said dislocation (like it is said that every action we make or could have make causes an alternate universe to come into existence). In either case it seems unlikely that there would be such a major difference between the two universes before Nero that Archer wouldn't have been the first captain if he was in the other did in the other. Now, since Nero and Spock appeared into a time between Archer and Picard, you could argue that their appearance caused the Borg never to travel back in time to the time of first contact, and thus Archer didn't encounter the Borg... but that would mean that either ENT didn't happen in the NuTrek universe either (or if it did, it simply happened before the events of the new movie took place, which then changed the universe... which would mean it can't really be NuTrek), or their appearance didn't prevent that from happening (unlikely, even given how illogical time travel often is, since the future was very radically altered from that point on).
Besides, if we completely dismiss Enterprise, there's no convincing evidence whatsoever that anyone in the Federation knew of the Borg before "Q, Who?". The most feasible way the Hansens knew about them would've been through the events in Enterprise (which still doesn't really explain the detailed cube model).
Also, why would the events in "Q, Who?" have caused the Borg to head to the Alpha Quadrant, when the Borg had already by that time assimilated humans (meaning at least the Hansens) and thus knew quite a bit about them, which should have already caused them to "come for more" if they wanted to?
Really. Sci-fi writers need lay off the time travel. It causes nothing but headaches. It's nothing but a cheap copout that inevitably leads to continuity errors when used in such a major role as in VOY, ENT and even TNG (can't recall if DS9 had much time travel).
Hell, I can't even make a coherent post about this, that's how illogical it all is
