How do we know Jesus is the fulfillment of the Isaiah prophecy?

In Luke 4:21, upon reading from the scroll of Isaiah, Jesus declared, 'This day is this scripture fulfilled in your ears,' referencing Isaiah 61:1-2. This fulfillment outlines His mission to preach the gospel to the poor, heal the brokenhearted, and proclaim liberty to the captives. By explicitly stating that He is the realization of this prophetic declaration, Jesus asserts His divine authority and messianic identity. The significance of this claim is profound, as it reveals His purpose and assurance that salvation is available to those who recognize their need for Him, establishing a clear connection between Old Testament prophecy and New Testament reality.