Shakespeare certainly does portray spontaneity of love as a theme in As You Like It, and Celia and Oliver falling in love certainly is one example of a spontaneous romance.
Oliver appears to have fallen in love with Celia as Aliena the first moment he sees and speaks with her, and Celia seems to quickly reciprocate his feelings and agree to marry him. However, it is not Oliver's looks so much as her knowledge of his newly changed character that incites Celia's feelings of love for Oliver. As we learn when Rosalind first falls in love with Orlando in the first act, both Oliver and Orlando are sons of Sir Rowland de Boys, a courtier that Rosalind's usurped and exiled father dearly loved and admired, as well as the rest of her father's court. Since it is commonly agreed upon that the "apple does not fall far from the tree," meaning that offspring usually have characteristics that are similar to their parents' characteristics, we know it is not a stretch for Celia to see Sir Rowland's characteristics in Oliver, even though Oliver did not seem to possess them at the beginning of the play. While Oliver admired his youngest brother's attributes, jealousy over his brother's attributes turned him into a very vicious person, or an "unnatural" person, as Celia phrased it (IV.iii.122). Nevertheless, at the point in the story that Celia and Oliver fall in love, Oliver has just gone through a major character change. Orlando sacrificed his life for Oliver, which helped Oliver realize his love for his brother, transforming him into as caring of a person as their father, Sir Rowland. Hence, when Celia spontaneously falls in love with Oliver for the first time, she is not necessarily falling in love with something trivial like his looks, she is falling in love with what she believes to be his character. We learn about the qualities of Sir Rowland all throughout the beginning of the play, but especially in Rosalind's comment to Orlando:
My father loved Sir Rowland as his soul,
And all the world was of my father's mind. (I.ii.235-36)
Hence we see that unlike other instances of love at first sight, or spontaneous love, Shakespeare is portraying Celia's lover for Oliver as being based on rational reasons rather than trivialities.
Their love could be described as the 'first sight love'. Both the couples did not make any deliberate mutual effort to impress. However, Silvius was at the back of Phebe for a longer period. It is substantiated from Act II Scene IV. He says to Corin :
But if thy love were ever like to mine-
As sure O think did never man love so-
How many actions most ridiculous
Hast thou been drawn to by thy fantasy?
O thou didst then ne'er love so heartily.
If thou remember'st not the slightest folly
That ever love did make thee run into,
Thou hast not lov'd:
Or if thou hast not sat as I do now,
Wearing thy hearer on thy mistress' praise,
Thou hast not lov'd:
Again in Act III Scene V, Silvius goes beyond the limit to praise the girl whom he loves. But, he is not anwered in the same coin by Phebe. Discovering this, Rosalind scolds Phebe for the lack of emotions. On the contrary, Phebe falls in love with Ganymede, without knowing he (she) is Rosalind. In the Act V Scene IV, the fact that Ganymede is Rosalind revealed. Then all of a sudden Phebe develops love towards Silvius. In this very scene she says to Rosalind,
If sight and shape be true,
Why then, my love adieu!
It means, if what my eyes are seeing arnd corresoponding with the shape(bodily structure) then Goodbye to my previous love. Without giving second thought, she accepts Silvius, which is spontenous.
Celia and Oliver's love affair is truly 'Love at first sight' Orlando is surprised for the same and questions his brother how it could be like that.
In Act V Scene 2 Orlando says:
Is't possible that on so llittle acquaintance you
should like her?That, but seeing, you should
love her? And, loving, woo? And, wooing, she
should grant? And will persever to enjoy
It means with short familiarity can anyone like someone? And just by seeing one should love? and just after loving one should go for courtship? And moreover how is it just after your proposal Celia gave her immediate consent of her? And how is it, just after getting consent, both are planning to marry?
So, with the above illustration, it is very clear that the love between these were spontenous save Silvius.