Well, fate may be too strong for some of these examples—some might be better called coincidences—but how about the following?
Act I, scene 1
: Both Lord Capulet
and Lord Montague
happen to enter as their men are fighting.
Same scene: the prince
enters as well (very convenient for the plot).
Act I, scene 2: Juliet's sisters are dead. (Why is this fate? Because it makes her father hesitate to marry her off to Paris, leaving more of an opening for Romeo.)
The same scene: the Capulet servant can't read, and it just happens to be Romeo who he bumps into, letting him learn about the party (where he'll meet Juliet).
Act I, scene 2: Romeo sees Juliet before being introduced, allowing him to fall for her without knowing she's a Capulet (that knowledge might block his love).