The question is looking for anything in the text that lends itself as a reason for this being Jesus' first miracle; also whether there is any indication within the text as to why this particular event marks Jesus' first recorded miracle.
The text selected is chapter 2 of John's gospel, the first 11 verses, but that immediately requires a problem being flagged up. We all know that John did not put any chapter or verse numbering in his text. When we read the verses immediately prior to the selected text, then we can find answers to those questions, because they set the scene and give the reasons for what then happened. Having grasped the context that led to this first sign, then we can learn especially from Mary matters of significance.
What had first happened was the baptising of Jesus by John the Baptist, and some of those who had been baptised then following Jesus. They had been prepared to recognise Jesus as "the Lamb of God who takes away the sin of the world" as the Baptist testified, having seen the Holy Spirit descend on Christ." He had witnessed that; they believed his testimony. John added that he "knew him not: but that he should be manifest to Israel, therefore am I come baptizing with water". That is a reason for why the first sign was performed three days after the Baptist was quizzed by priests and Levites from Jerusalem and said those things.
Note that when two of the Baptist's disciples heard his testimony and believed it, they started following Jesus who then invited them to stay with him. The next day Andrew called his brother to also follow Jesus. The following day, Jesus found Philip and called him to be a follower. Philip, in turn, found Nathaniel who was skeptical, doubting if anything good could come out of Nazareth. Jesus demolished that wrong idea by making a declaration about Nathaniel (requiring divine insight) that astonished the man, who was then told by Jesus that he had seen him sitting under a fig tree, before Philip called him. That was miracle enough for Nathaniel to proclaim Jesus as the Son of God, the King of Israel.
Such a miracle was a personal sign to Nathaniel, but it was not a manifestation to Israel. That would require the sign-event at Cana the next day when a large gathering who probably knew very little about Jesus were present to witness it.
As well as that sign-miracle getting the attention of the crowd, it bolstered the disciples' faith in Jesus as the Son of God, who, the day before, had told Nathaniel (and the few others present) that they would see greater things, and afterwards, they would "see heaven open, and angels of God ascending and descending upon the Son of man" - reminding them of the vision of Jacob's ladder (Gen. ch. 28). The sign-miracle at Cana was the start of such "greater things".
Then begins the selected text. Yet already we should see the direct connection with disciples being prepared, then called to follow Jesus as the Messiah. This now leads into the significance of Mary in connection with the sign-miracle her son, Jesus, chose to perform.
From Mary, we learn how her heart was well prepared, from knowing the miraculous message of the angel, the miraculous birth, the boy Jesus aged 12, at the temple, and no doubt many other things not recorded. Yet despite that, her words to Jesus at the wedding, received a strange response. What is the significance of this part of the account? Let me quote from this book, which refers first to what her 12-year-old son said to her at the temple:
"Deep, deep down, the sayings of her son, Jesus, penetrated into the
heart of his mother. And she was not offended. At first, she had made
an enquiry. But on hearing the response, the word of Christ fell upon
good ground.
Nor was she offended when he, now grown, responded to her statement,
'They have no wine', with, 'Woman, what have I to do with thee? Mine
hour is not yet come.' No, not offended. 'Whatever he saith unto you,
do it', she commanded unto the servants. Spiritualities took
precedence. She accepted the rebuke. She submitted, correcting the
situation. She took no offence. For the mother of Jesus had long kept
things in her heart.
Long before, thirty years before, all who heard the report of the
shepherds of the angels and the babe in the manger, 'wondered' at
those things, Luke 2:18. And many still do, admiring, marvelling,
wondering. It goes no deeper. But Mary, the rather, kept all these
things and pondered them - in her heart.
...No, not offended; but retaining all that she heard in her heart,
she pondered. And accepted rebuke and correction, when it was applied
to her. Such is the ground, prepared by the Preparative Messenger,
wherein the word of God, when it falls there, takes deep, deep root.
And, in due time, with patience, brings forth abundantly." The
Beginning of the Gospel, Nigel Johnstone, pp. 51-52, Belmont, 2012
http://www.belmontpublications.co.uk
So, let no one think critically of Mary. We could do with learning from her.
Further, those present at Cana whose hearts were prepared to receive the words of Christ, which are life and truth, saw what the sign was pointing to - Christ as Messiah. If a sign is misunderstood, the wrong direction will be taken. One needs to know what to look for, with a sign - to what it is pointing. The sign is not the thing itself. No sign points to itself. At Cana, the miracle-sign pointed to Christ as the foretold Messiah. For those whose hearts are prepared to accept this, they will set out on the right direction, which is to follow Christ, wherever he goes. They will see and understand the other signs along the oft-difficult way. And all of those heaven-sent signs keep our eyes set on Jesus, the Son of God. But for many of those at Cana, whose delight was in splendid wine miraculously produced, they did not consider what that sign was pointing to; they were so taken up with the miracle-sign and did not consider who it was pointing to as sent from God, and all because their hearts were not prepared, as was Mary's.
Answer in Summary: Jesus had started gathering disciples and, both for their benefit to reassure their initial views (John 1:41; 45; 49), and to start manifesting himself to Israel (John 1:33; 50-51), Jesus began his miracles at Cana. This was the start of his pubic ministry.
