As @entwyfhasbeenfound said it will set the tone for what follows. I would approach the start as the hook, a chance to answer the question ‘what’s this show about and why should I stick around?’
It can be full of action with explosions, car chase, fight scene, battles etc
It can be suspenseful, piquing the viewers enough to want to continue watching to find out what happens next. Perhaps a mystery or a killer on the loose, that will require a longer commitment before the case is solved or the killer caught.
Just a couple of opening types to hook in viewers.
If we start with them falling in love, it would take a long time before we even reach the first occurrence of the supernatural phenomena.
If we start with them flying to Seoul we can then shift the romance in a flashback as you suggested. I’m thinking maybe, couple surprise parents, parents react, Ha-Neul recount her trip to parents, [mulberry farm, how they met, fell in love and married] in a recounting flashback ‘mini series’ then jumping back to the main drama Ha-Neul concluding the recount and the main drama continues.
The flying back to Seoul opening will allow us to immediately introduce phenomena.
I already have an idea but I want to see other people’s ideas for the opening scene before posting my version. (reasonably detailed for that all important first impression)