The sun soon emerged from behind the clouds.
まもなく (or 間もなく) is a terrible collocation with 現れてきた (in a past progressive form). 間もなく in this sentence can function only as “in the near future”. So, 太陽がまもなく雲の陰から現れてきた means “The sun would be emerging from behind the clouds in a moment.” It’s a grammatically broken sentence in Japanese… I would propose:
Note 1: You cannot replace 間もなくして with 間もなく in this sentence.
Note 2: Swapping the word order like this makes the whole sentence more natural.