Due to the nature of tabletop RPGs, a campaign will often start with a random group of strangers. Here are some ways to get them adventuring together, without resorting to the old Tavern trope.
With regard to the plot "Sleeping Mines of Elathon":
You manage to get the water wheel in the mine working which operates a pump to clear the flooded lower levels. As you explore the dank tunnels of the lower galleries, you can hear the creaking of the wheel above. You enter a low-ceilinged passage and are crawling on your backs, when the creaking stops. The water starts seeping wetly around the back of your head...