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).