The exposition in this passage begins with the sentence "It was 2 p.m. on the afternoon of May 7, 1915." This is because the exposition is the part of the story that introduces the setting, characters, and conflict.
So, the setting is the sinking of the Lusitania, the characters are the young girl and the mysterious stranger, and the conflict is the sinking of the ship and the fear and uncertainty that it causes.
The following sentence, "while the boats were being launched with all possible speed," suggests that there is a race against time to save the passengers and crew. The sentence "The women and children were being lined up awaiting their turn" further highlights the urgency of the situation and introduces the young girl who is standing alone, slightly apart from the rest.