[@Carlsberg] My original idea around this problem was to have Parfex's and your characters attend the same school (maybe instead of school your characters attended MMA classes or something?) but personally didn't know each other. Between the two of you, you could can decide on some kind of activity that the two of you would've taken part of during school that would've started the rivalry. But then at 18 your character would go and join the military while Parfex's would have found the meteorite that gave him his powers which would eventually lead to the time jump for his character. As his character disappears at age 18 and doesn't reappear until 6 years later at age 24 due to his powers you wouldn't be able to fight him at 19/20.

EDIT: Maybe instead of school your characters attended MMA classes or something?