Olivia happens upon Sebastian, thinking him to be Cesario, while he is engaged in a brawl with Toby and Andrew. Since the setting is during a time of festivity, drunkenness and brawling were a part of normal behavior; however, Olivia steps in to stop the fight and apologizes for her uncle's behavior. For Olivia, this isn't the first time she has met Sebastian because she thinks he is Cesario. Hence, her spur-of-the-moment proposal jumps into line with the wild thinking of the festival period but also supported by previous meetings she thinks she has had with him. Sebastian, swept away by Olivia's social status as well as her beauty, deems the match perfect. It's not every day a man is proposed to by a beautiful gentle-woman. Having lost everything thing anyway, Sebastian follows his "heart" and marries Olivia immediately.
Sebastian's reasoning behind his response to the proposal:
What relish is in this? how runs the stream?
Or I am mad, or else this is a dream:
Let fancy still my sense in Lethe steep;
If it be thus to dream, still let me sleep!"(IV.i.58-61)
He seems to be going with the flow of moment and taking advantage of what fortune brings him.