How do we know that Jesus' ministry included Gentiles?

In the Gospel of Matthew, the account of the Canaanite woman demonstrates that Jesus' reach extended beyond the Jewish people. When this woman cried out for help, acknowledging Jesus as the 'Son of David,' she exemplified faith that recognized Jesus as Messiah despite her Gentile background. While Jesus initially seemed to emphasize His mission to Israel, this encounter signifies that His work was ultimately for all humanity. The woman’s great faith illustrates that Gentiles could access God's mercy, foreshadowing the Great Commission where Jesus commands His disciples to make disciples of all nations, affirming the inclusivity of God's grace and salvation through faith.