Many different scenes in Twelfth Night can be said to change the fate of characters. Viola's fate is changed the moment she decides to disguise herself as a boy and work for Duke Orsino; Olivia's fate is changed the moment she decides to admit Cesario as Orsino's messenger into her home; We learn that Orsino's fate has been changed when we learn he has not only admitted Viola as Cesario into his home to allow her to work for him but has taken a great liking to her as a boy; Malvolio's fate is changed the moment he decides to break up the singing, drinking party in Act 2, Scene 3; Sebastian's fate is changed the moment he steps onto the grounds of Illyria, and likewise Olivia's fate is changed the moment she confuses Sebastian for Cesario. The list continues on and on from there. Hence, we can see that in pretty much every single scene, a decision a character makes changes what will happen to that character in the future. Let's look at Viola's decision in Act 1 as an example.
After arriving in Illyria, Viola became well aware of her now very vulnerable position. Her father passed away when she was only thirteen, and possibly even her mother before him, and now she believes her one remaining guardian, her brother, drowned in the shipwreck she has just survived. Not only is she now an orphan, she is also a wealthy noble woman and knows full well how easy it would be for someone to take advantage of her situation. Hence, one thing she longs for is a safe haven to hide in until she feels it will be safe for her to expose her true identity as an orphaned, wealthy noble woman, as we see her explaining to the sea captain who rescued her:
O that I served that lady [Olivia]
And might not be delivered to the world,
Till I had made mine own occasion mellow,
What my estate is! (I.ii.43-46)
However, when the captain warns her she would not be admitted into Olivia's household due to the fact that Olivia is rejecting all company while she is in mourning, Viola next decides to try and work for Duke Orsino disguised as a eunuch in order to protect her true identity as a vulnerable noblewoman. More importantly, we know that Viola has grown up hearing from her father about Duke Orsino's character and has already come to greatly respect and admire him. Hence, the decision to go to work for him opens up the doors to the possibility of falling in love with him, forever changing her fate.