OK, let’s try putting all together, here. Dates may be Obi Wan because of the difference between the TV calendar and the real calendar, and also because of my overly geeky but failing memory.
2364 – Enterprise-D launches.
2365 – in episode “Q Who?”, Q sends the Enterprise across the galaxy to the Delta Quadrant, introducing the Federation to the Borg. Guinan warns Picard to get out now, because the Borg destroyed her culture, the El Aurians.
2366 – Picard is assimilated by the Borg at end of 3rd season, rescued at beginning of 4th.
2371 – Voyager is lost in the Delta Quadrant.
2372 – The Borg Queen travels back in time to 2063. This time is significant, because it is the date of the first warp flight by human beings. A Vulcan science vessel happens to be in the Sol system at the time and notices the test, leading to first contact between humans and another alien species. The Borg Queen intends to prevent this and therefore prevent the Federation from ever happening.
2152 – A Starfleet research team discovers Borg drones frozen in the Arctic. They of course manage to reactivate themselves and assimilate the research team. Eventually, they get off-world and are destroyed by the Enterprise-01, but not before they manage to send a subspace signal to unknown coordinates in the Delta Quadrant. The message will not be received until c. 2360.
The options for wiggling out of canon issues are two-fold.
[ol][li]The records from this time in the past (from the view of the 2300s) are somewhat spotty. This is a believable option, as many references in TNG lead one to believe that there have been only five Enterprises, which do not include the NX-01. Of course, it’s difficult for me to believe that a vessel that made so many supposedly important contributions to the furthering of Starfleet could be so completely forgotten. Maybe something they did was so incredibly horrible that their entire existence was erased from the records in the interest of interstellar harmony. [/li]
[li]Or, because of the events in First Contact, all of Star Trek canon up through that film are suspect, because the past has been changed. As often as Bermaga approved the Reset Button in Voyager (meaning plots in which all character development and growth is rendered null due either to time travel within the episode or hallucinations from hostile species), this is certainly plausible.[/ol][/li]
To keep my wits about me, I go with explanation number 1.