God's Law already had three tests for divine revelation: never contradict existing Scripture or commands; never contradict God's unchanging character; never fail. All prophets, or messengers of God, must meet those requirements. The teachings and power of Jesus and the Apostles passed all three tests.
God promised to save humanity from our sin. This Savior would be God in the flesh, born of a virgin, be from Bethlehelm, of a specific tribe, work miracles, be rejected by his people, and die for our sins. Last two are in Isa. 52:13-15 and Isa. 53. God told David the same Messiah would reign over an everlasting kingdom, starting on Earth. That's despite dying for our sins. That implies God will raise the Messiah from the dead.
God lays out specific prophecies like these so we don't have to guess who to trust. Jesus fulfilled all of them in His life. (Full list.)
In contrast to this, other religions had no prophecies, contradicted the Word, contradicted God's character, and/or had failures. Even one failure was enough to disqualify a prophet. God's own power ensured they would succeed.
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