I guess kinda like the time traveler's wife. Where the lead meets their future wife/husband when they're young and the other party is rather aged. I'm also okay if it's just a prediction or vision or similar.

Not exactly what you described, but in the ballpark:

  • W - The ML is a fictional character who was originally dreamed up by the FL when she was a kid and then adapted + fleshed out by her father in a best-selling manhwa series that he wrote. The FL enters the world of the manhwa and ends up entering into a fake marriage with the ML for her protection. And of course they end up dating for real later on.
  • The King: Eternal Monarch - When the ML is a kid, he is nearly assassinated. The person who saves him drops an ID badge belonging to the adult FL. The ML considers her his saviour and searches for her. The adult FL lives in a parallel world, and the ML meets her when he is grown up. It turns out the person who saved the young ML was his own adult self, who was carrying the FL's ID badge.
  • A Korean Odyssey - The ML is an immortal. When the FL is a little girl, she stumbles upon the ML's prison and is tricked into setting him free. They cross paths again when the FL is an adult. They don't get married in the drama, but they do date and at one point they get tangled up in a wedding ceremony

Also:

  • Tomorrow With You
  • Another Oh HaeYoung 
  • Soulmate (2006)
  • Kiss Sixth Sense
  • Meet me at 1006
  • Sisyphus: The Myth
  • While You Were Sleeping
  • Marry him if you dare - though this was a disappointing drama