Assuming that the characters come first however, there should still be a multitude of ways in which those individuals in particular can meet. If they're going to be sharing page space, then they probably have some areas of interest in common, and others that contrast each other. Either way those intersections are leads to a meeting point. Are they both avid readers, or does one like to read and the other need to look something up in a reference book? Does one play golf and the other walk a friend's dog near the golf course? Have they both been sent to the same dull lecture by their respective employers?
I meet new people every day. Most of the time these encounters are more likely to be fleeting than to lead to a close relationship and/or a quest to find the Holy Grail, but they can all provide inspiration for how things could have gone for two different people under similar circumstances.
So today's question is: what real or fictional meeting sticks in your mind? Either because of what happened next, or what could have done? Could a story be built around that meeting?