After Jesus was identified as the Messiah and baptised by John, and after he had collected some disciples; the first incident in the Fourth Gospel is the marriage at Cana, the turning of water into wine; which is described as the beginning of the miracles.
The marriage at Cana describes Jesus's wedding (i.e. it identifies Jesus as the bridegroom - this interpretation being confirmed later in John 3:29). And then Jesus does his first miracle; why then?
My understanding is that the marriage was the moment when Jesus assumed his ministry - at the late age of thirty. I assume that the baptism by John what made it possible; the marriage was what made it happen. This is my interpretation of the governor's comment, addressing Jesus: 'thou has kept the good wine until now'.
Presumably, this was why this miracle was done at this time - as a sanctification of the marriage; that this marriage was, compared with an ordinary marriage - symbolically and literally - as wine is to water.
Otherwise, this miracle of transformation seems rather a rather feeble, even trivial, achievement; at least by comparison with Jesus's miracles of healing. Yet we are told that it 'manifested forth his glory' - so there must have been something very important about it.
(Note: Unfortunately, I get the feeling that there is something wrong with the Biblical text of this episode - especially 2: 3-5, where there is both an impression of alien interpolation and of omission.)
Note added: I suspect that the marriage of Jesus being followed by the performance of miracles is related to the dyadic nature of fully creative divinity. This is implied by Mormon theology, with its assertion that celestial-eternal marriage is required for full divinity; and full divinity is characterised by the procreation of spirit children. This would suggest that it was necessary that Jesus was celestially-married in order that he would attain full divinity, with the same fullness as his Father (albeit, the Son lives and creates within the creation of the Father).
 And the third day there was a marriage in Cana of Galilee; and the mother of Jesus was there:
 And both Jesus was called, and his disciples, to the marriage.
 And when they wanted wine, the mother of Jesus saith unto him, They have no wine.
 Jesus saith unto her, Woman, what have I to do with thee? mine hour is not yet come.
 His mother saith unto the servants, Whatsoever he saith unto you, do it.
 And there were set there six waterpots of stone, after the manner of the purifying of the Jews, containing two or three firkins apiece.
 Jesus saith unto them, Fill the waterpots with water. And they filled them up to the brim.
 And he saith unto them, Draw out now, and bear unto the governor of the feast. And they bare it.
 When the ruler of the feast had tasted the water that was made wine, and knew not whence it was: (but the servants which drew the water knew;) the governor of the feast called the bridegroom,
 And saith unto him, Every man at the beginning doth set forth good wine; and when men have well drunk, then that which is worse: but thou hast kept the good wine until now.
 This beginning of miracles did Jesus in Cana of Galilee, and manifested forth his glory; and his disciples believed on him.(...) John. 3:  John answered and said, A man can receive nothing, except it be given him from heaven.
 Ye yourselves bear me witness, that I said, I am not the Christ, but that I am sent before him.
 He that hath the bride is the bridegroom: but the friend of the bridegroom, which standeth and heareth him, rejoiceth greatly because of the bridegroom's voice: this my joy therefore is fulfilled.