Genesis (γένεσις) refers to birth, origin, or the beginning of something. In Matthew 1:1, it translates the title of the genealogy of Jesus as "the book of the genesis of Jesus Christ" — deliberately echoing the LXX title of the first book of the Bible. In James 1:23 it refers to one's natural face; in James 3:6 it refers to "the cycle of nature."
Matthew opens his Gospel with genesis as a deliberate allusion to Genesis 1:1 — signaling that the story of Jesus is a new creation narrative, a new beginning. The genealogy of Matthew 1 traces God's redemptive faithfulness through generations until the ultimate new beginning arrives in Christ. In Him, personal genesis is possible — "if anyone is in Christ, he is a new creation" (2 Corinthians 5:17).