Assuming that the Federation we saw in the first five seconds of the movie was the same Federation that existed before history changed, then I would have trouble believing that Kirk could defeat the Borg we all know and loved and then loathed. (I will admit that if the Borg Queen continues to become more and more decadent, then her efforts to make Kirk Locutus Model -1.0 would result in Kirk ending the collective forever and the Borg Queen carrying his baby)
There is another option. Do we really know that much about the 23rd Century Borg? Perhaps they were significantly less technological empowered and dependent. We could, for example, have a story where the 23rd Century Borg show up after having heard about their descendants fun and games with Cochrane and then Archer to invade the Federation. Only they are far from the challenge. Instead of being a race of bionic zombies, they are just a race of zombies. Individual Borg are easy to kill. Individual (but much smaller than familiar) cubes are easy to destroy. But they can still adapt. Instead of having one cube smash 39 ships, we have one ship smash 39 cubes only to find that 300 more or coming and they are more prepared. The race is for Kirk and Spock to defeat them before they become too strong.