곧(got)
Indicates something happening very soon or immediately in the near future
When to use
Immediate occurrence, Urgent notification, Scheduled imminent arrival
The nuance
곧 points to a very near future from the present moment, emphasizing immediacy or urgency.
머지않아(meo-ji-an-a, meojiana)
Indicates that something will happen after a short while, with slightly more time than 곧
When to use
Near future prediction, Time allowance exists, Relatively relaxed notification
The nuance
머지않아 is used when there is slightly more time left than 곧, but still refers to the near future.