John is purposeful to include a chronological element to the beginning of the events of the Gospel by making three consecutive "the next day" (τῇ ἐπαύριον) statements, which has the effect of marking the first day in the sequence:
[The first day]: John the Baptist gives his testimony to priests and Levites who from Jerusalem.
"The next day" (1:29) [1st or 2nd day]: John the Baptist sees Jesus and identifies Him as "the Lamb of God who takes away the sin of the world" and "the Son of God."
"The next day" (1:35) [2nd or 3rd day]: John the Baptist sees Jesus a second time and calls Him "the Lamb of God." Two of John's disciples (Andrew and another) leave John to follow Jesus.
"The next day" (1:43) [3rd or 4th day]: Jesus decided to go to Galilee.
John's discussion with those sent from Jerusalem took place the day before the first "next day." So Jesus decided to go to Galilee on either the 3rd or the 4th day of this sequence, depending on which day is taken as the point at which to begin the count. Therefore, "the third day" which begins chapter 2 cannot be counted from the beginning of the Gospel. This leads some commentators to believe the third day is counted from the day referenced in 1:43.
There is a practical consideration which must be considered: the wine had run out. If the events are meant to take place during a week long celebration, it is unlikely the wine would be out by the first or even second day. Therefore a timeline connected to any of the previous "next days" of Chapter 1, is unlikely, instead, the "third day" should more likely be seen in reference to the third day of the week of festivities. This too is unlikely since the events seem to be described as taking place on the banquet of first day. (The comments made by the master of the ceremony make more sense if he was tasting wine during the first meal, not after several days of drinking.)
Because there is a specific mention of time to begin the Gospel, John's "on the third day there was a wedding..." should be considered as intentionally vague, or purposely ambiguous in order to cause the reader to question what is meant. This leads Craig R. Koester to see the symbolic nature of the reference:
The pregnant reference to Jesus' "hour," however, demands that the sign be understood in light of Jesus' passion (John 2:4). Cana was the first (archē) of his signs, and the cross marked the culmination (telos) of his works. The presence of Jesus' mother at Cana and the cross - and only in those two places in John's Gospel (2:1-12, 19:25-27) - reinforces the idea that the glory manifested in the wine and in Jesus' death must be understood together....Perhaps even the comment that the wedding took place "on the third day" may point in this direction, since the three days from his crucifixion to resurrection are mentioned in the next scene as well (2:1, 19-20). Jesus' messiahship would lead to Golgotha and his glorification would be accomplished through crucifixion and resurrection. The divine favor revealed by his gift of wine was a prelude to the gift of his own life.1
The emphasis is not when to start counting, but on "the third day." Therefore, after third day, the disciples believed in him (2:11); after which they were together for a few more days (2:12). In this case, John has presented the first sign in a way following the sequence of the glorification of Jesus:
Cana - Wedding Jerusalem - Passover
[The first day] Crucifixion
The third day - water to wine Resurrection
+ Disciples believed in Him + Disciples received the breath of Him
Stayed a "few days" in Capernaum Met disciples by the Sea of Tiberias (John 21)
The ambiguity of the date of the miracle in Cana, establishes the unambiguous point in time at which the first disciples first believed in Him (on the third day). This creates two symbolic parallels. One is that of the first disciples first receiving the Holy Spirit (three days after His crucifixion). Another parallel connects the events of chapter 1 which are spread over three days, during which the first disciples wanted to see where Jesus was staying before following Him to Cana to attend the wedding (to which they also were invited).
Adding "on the third day" brings the entire sequence from John the Baptist's pronouncement into the symbolic nature of the sign at Cana:
First "three" days:
Behold the Lamb of God who takes away the sin of the world (1:29)
This is the Son of God (1:34)
Behold the Lamb of God (1:36) - Rabbi, where are you staying? (1:38)
So they came and saw where he was staying, and they stayed with him that day (1:39)
Follow Jesus to the wedding (1:43) to which they were invited (2:2)
On the third day:
On the third drink the best wine at the wedding banquet and believe in Him (2:10)
- Craig R. Koester, Symbolism in the Fourth Gospel, Meaning, Mystery, Community, Fortress Press, 1995, pp. 80-81