The only thing I did like about Cochrane in that movie was that when you get a change to visit a hero you have held in high esteem your whole life only to discover that they were nothing like you imagined. Once you get past that one surprise you do wonder how this man could have a remote chance of creating what he was famous for. Even if he was a full on Doc Brown genius, that base did not seem to have the facilities to produce a Warp craft.
Why go back to first contact in the first place. The Borg were interested in federation technology, why not visit Earth during the time of 'Q Who?'. Nobody would know what the Borg were still and assimilating the planet might take longer, but that Sphere with the queen could pretty much do anything they wanted to do before the Federation figured out what was going on.