Jesus taught that through him comes our purification/righteousness & so eternal life.
• E.g. Jn 1:29 — the Lamb of God [Jesus] who takes away the sin of the world!
• E.g. Jn 11:25 — “I am the resurrection and the life; he who believes in Me [thereby being purified] will live even if he dies,” cf. Jn 6:35, 8:12)
• E.g. Jn 20:31 — that believing you may have life in His name.
• E.g. Matthew 25:46 — These will go away into eternal punishment, but the righteous into eternal life.”
• Jesus accepted baptism by John the Baptist, and the gospels say John taught it. (see below)
For 3 examples from Paul's letters:
• Romans 6:4 — Therefore we have been buried with Him through baptism into death, so that as Christ was raised...
• Romans 8:11 — But if the Spirit of Him who raised Jesus from the dead dwells in you, He who raised Christ...
• 1 Corinthians 6:14 — Now God has not only raised the Lord, but will also raise us up through His power.
This is relevant because Jesus commissioned Paul, which is unlikely if Paul would just go on to just misrepresent a core part of Jesus's message. More than likely, given the weight of what he experienced and how he dedicated his life to it, Paul went on to represent Jesus and the Gospel with extreme care and accuracy.
Mt 3:11-12 — [John the Baptist said] The axe is already laid at the root of the trees; therefore every tree that does not bear good fruit is cut down and thrown into the fire. As for me, I baptize you with water for repentance, but He who is coming after me is mightier than I, and I am not fit to remove His sandals; He will baptize you with the Holy Spirit and fire. His winnowing fork is in His hand, and He will thoroughly clear His threshing floor; and He will gather His wheat into the barn, but He will burn up the chaff with unquenchable fire.” (cf. Jn 1:29 — the Lamb of God who takes away the sin of the world!)
This is relevant because Jesus accepted baptism by John the Baptist, which fits best with the hypothesis that John represented and understood Jesus (and his message) rightly.