At this point that requirement seems to be a bit more flexible then originally thought. If you recall Sasuke gained his Mangekyo when he saw itachi kill orochimaru the closest person to him (this is explained by tobi).
Based on this it's just an extreme emotional response upon witnessing the death of a close friend or loved one.
With this is in mind it could have been unlocked by any number of deaths over the years witnessed by Kakashi. Most likely either Obito or Rin.
This is some what of an inconsistency since so much time went by before we saw him use it as opposed to Itachi or Sasuke who seemingly used it shortly after unlocking it. But to be fair it didn't seem Sasuke knew he had it until amaterasu was triggered by Tobi's sharingan.
Taking all of this into consideration with the fact that Kakashi isn't an Uchiha and his sharingan has an especially high strain on his body, the best we can assume is that Kakashi's MS was unlocked early on but he wasn't able to push his body to the limits need to activate it (or discover he had it) until the time jump.
With little manga info given this is the best we can ascertain.