Second Clue: Luke 3:23
Luke 3:23 Now Jesus Himself began His ministry at about thirty years of age, being (as was supposed the son of Joseph), the grandson of Heli,
So you see, Jesus Himself was not quite 30 years old either when He started His own ministry.
But when did Jesus start His ministry?
Let's switch to the account of John the apostle. Several weeks before Passover in 28 AD, John the Baptist was already in full swing with his ministry, baptizing people in the Jordan river. That's why the priests and Levites noticed him and started questioning him. Read John chapter 1 verses 19 – 28:
John 1:19 Now this is the testimony of John, when the Jews sent priests and Levites from Jerusalem to ask him, “Who are you?”
20 He confessed, and did not deny, but confessed, “I am not the Christ.”
21 And they asked him, “What then? Are you Elijah?” He said, “I am not.” “Are you the Prophet?” And he answered, “No.”
22 Then they said to him, “Who are you, that we may give an answer to those who sent us? What do you say about yourself?”
23 He said: “I am the voice of one crying in the wilderness: 'Make straight the way of the LORD, ’ as the prophet Isaiah said.”
24 Now those who were sent were from the Pharisees.
25 And they asked him, saying, “Why then do you baptize if you are not the Christ, nor Elijah, nor the Prophet?”
26 John answered them, saying, “I baptize with water, but there stands One among you whom you do not know.
27 “It is He who, coming after me, is preferred before me, whose sandal strap I am not worthy to loose.”
28 These things were done in Bethabara beyond the Jordan, where John was baptizing.
The next day, John the Baptist baptized Jesus. See John 1:29-34:
John 1:29 The next day John saw Jesus coming toward him, and said, “Behold! The Lamb of God who takes away the sin of the world!
30 “This is He of whom I said, ‘After me comes a Man who is preferred before me, for He was before me.’
31 “I did not know Him; but that He should be revealed to Israel, therefore I came baptizing with water.”
32 And John bore witness, saying, “I saw the Spirit descending from heaven like a dove, and He remained upon Him.
33 “I did not know Him, but He who sent me to baptize with water said to me, ‘Upon whom you see the Spirit descending, and remaining on Him, this is He who baptizes with the Holy Spirit.’
34 “And I have seen and testified that this is the Son of God.”
From Jordan, after His baptism, He was led by the Spirit to the wilderness, and tempted by Satan for 40 days.
Then He went to Cana in Galilee where He reluctantly performed His first miracle by turning water into wine at the request of His mother.
When He performed His first miracle in Galilee, He hasn't started His ministry yet. Notice what He told His mother in John 2:3-4:
John 2:3 And when they ran out of wine, the mother of Jesus said to Him, “They have no wine.”
4 Jesus said to her, “Woman, what does your concern have to do with Me? My hour has not yet come.”
When He went to Nazareth, He was rejected by His own people. Afterwards, He went down to Capernaum with His mother and brothers and stayed there for a few days.
Then He went up to Jerusalem to observe Passover. Before Passover, He cleaned up the temple first of money-changers and traders. (John 2:13-16)
Evidently, this is the declaration of the start of His ministry. As we read in John 2:23
John 2:23 Now when He was in Jerusalem at the Passover, during the feast, many believed in His name when they saw the signs which He did.
So He officially started His ministry at Passover of 28 AD. This makes perfect sense, since God is using His festivals as markers for important events. Also, at this point, He was a little over 29-1/2 years old. This is consistent with what Luke said in Luke 3:23 that He was about 30 years old when He started His ministry, meaning not quite 30 years old yet.
Jesus observed another Passover in the middle of His ministry in 29 AD (John 6:4)
John 6:4 Now the Passover, a feast of the Jews, was near.
Then in 30 AD, He became the Passover sacrifice Himself. As the blood of the symbolic passover lamb saved the Israelites from death in Egypt, the blood of our true Passover Lamb saved mankind from the ultimate death penalty pronounced upon Adam when he sinned.
We can read the account of Jesus' sentencing to death beginning in John 19:13-16
John 19:13 When Pilate heard these words he brought Jesus outside and sat down on the judgment seat in the place called “The Stone Pavement” (Gabbatha in Aramaic).
14 (Now it was the day of preparation for the Passover, about noon.) Pilate said to the Jewish leaders, “Look, here is your king!”
15 Then they shouted out, “Away with him! Away with him! Crucify him!” Pilate asked, “Shall I crucify your king?” The high priests replied, “We have no king except Caesar!”
16 Then Pilate handed him over to them to be crucified. So they took Jesus, (New English Translation)
Notice the parenthetical comment by John "(Now it was the day of preparation for the Passover, about noon.)" John was making a side comment that starting at about noon time that day, as had been the practice every year, the Passover lamb were being prepared to be slaughtered that afternoon. This is discussed more in detail in the article "When was the passover sacrificial lamb slain?"
Pilate handed Jesus to the Jews early morning. Then at nine o'clock Roman time or third hour Hebrew time, He was already put up on the stake (Mark 15:25)
Mark 15:25 Now it was the third hour, and they crucified Him.