Read all four gospels together, the Wedding of Cana took place not long after Jesus' Baptism. His Baptism was happened at Bethany on the other side of the Jordan, where John was baptizing (John 1:28). At this location, we can imagine that Jesus should have visited Jerusalem, likely for the Feast of Tabernacles, and October is a good season, not too hot, not too cold for Baptism and Wedding taken place.
Immediately follow the Wedding of Cana, John's gospel immediately jumped to the next visit to Jerusalem, for the Passover (John 2:13). A few events happened before he went back to Cana, Galilee, include;
- Jesus teaches Nicodemus (John 3:1-15)
- Jesus and His disciples baptized people in Judean countryside (John 3:22-36)
- Jesus left Judea and talks with a Samaritan Woman, and stayed in Samaria for two days (John 4:1:41)
Then finally, Jesus arrived Galilee and visited Cana again, where a "certain royal official (NIV)/ certain nobleman (KJV)" whoes son lay sick at Capernaum, begged Jesus to go to Capernaum to heal his son (John 4:46-54).
Now, the OP had asked a good question. In between these two signs, there is a significant time lapse. Did Jesus perform any miracles during the time?
My answer is "Yes", but in John's perspective he did not call them a sign. Then why was it?
After the wedding of Cana, Jesus went to Capernaum with his disciples (John 2:12). Reading all four gospels together, it is quite clear that Capernaum was a base of Jesus' Ministry. A few healing, exorcism were happened in Capernaum and its surrounding, below were likely happened in between these two signs
- Jesus drove out a demon on Sabbath in Capernaum (Mk 1:21-28; Luke 4:31-37)
- Jesus healed Peter's mother-in-law in Capernaum (Matt 8:14-17; Mk 1:29-34; Luke 4:38-41)
- Jesus healed a paralyzed man on sleeping mat in Capernaum (Matt 9:1-8; Mk 2:1-12; Luke 5:17-26)
- Jesus healed a man with a shriveled hand on Sabbath (Matt 12:9-14; Mk 3:1-6; Luke 6:6-11)
- Jesus healed the multitudes (Matt 12:15-21; Mk 3:7-12; Luke 6:17-19)
So why was John not taken the above as signs?
It is because the healing of the "certain nobleman's son" was done without the presence of Jesus.
Reviewing the seven signs of John, all indicate a status of impossible becomes a status of possible, a sign of undisputable divine intervention.
- Turn water to wine is a change of substance state, illustrated God's almighty power
- Healing a nobleman's son remotely illustrated the power of divine word.
- Healing a man disabled for 38 years at Bethesda pool shocked the Jewish leaders. Jesus proclaimed His authority on Sabbath.
- Feed the five thousand - an allusion of Manna
- Walked on Water - a requirement of Faith
- Heals a man who was blind since birth - as Jesus corrected a tradition bias of the Jews; John 9:3 “Neither this man nor his parents sinned,” said Jesus, “but this happened so that the works of God might be displayed in him. 4 As long as it is day, we must do the works of him who sent me. Night is coming, when no one can work. 5 While I am in the world, I am the light of the world.” (NIV)
- Lazarus resurrection - an allusion to salvation.
These seven signs were specific chosen by John, to affirm Jesus is God, a meaning much more significant than the miracles itself.