Very interesting question. Of course, you need to remember that this play is all about characters falling strangely, suddenly and inexplicably in love with other people - often apparently against their better judgement in a way that drives them to folly or absurdity. Just consider the way that "love at first sight" is introduced by the love-sick Orsino:
O, when mine eyes did see Olivia first,
Methought she purged the air of pestilence.
That instant was I turned into a hart,
And my desires, like fell and cruel hounds,
E'er since pursue me.
Note similarly what Olivia says when she falls in love with Caesario:
Even so quickly may one catch the plague?
Methinks I feel this youth's perfections
With an invisible and subtle stealth
To creep in at mine eyes.
What is interesting in both of these quotes is how love is described. Orsino describes his sudden love for Olivia in a very violent manner - he becomes subject to his desires, so much that they constantly haunt and dominate him. The metaphor of the pack of dogs hunting the deer (the "hart") suggests that there is something out of control in his love - just as a pack of dogs when they have the scent go crazy and pursue their quarry, so we see a love-stricken Orsino in Act I scene i, who is mastered by his emotions and out of control. Similarly Olivia describes her "love" as something insidious, "creeping" and overpowering. She is not able to control her response but describes what is happening to her in terms that relate love to a thief or an assassin that creeps up on us with "invisible and subtle stealth" to overpower us.
Both these metaphors stress how love comes upon us like a "plague" or a "sickness" as it is described by other characters. We have no control over it and it just happens to us, seemingly apart from any conscious choice of our own. Thus love at first sight is a central theme of the play, but it speaks more of infatuation, of how dangerous it can be, and how it can rule us, and and how it can cause us to make fools of ourselves in the name of "love".