Which Gospel begins with a genealogy?

Answer: Matthew

Matthew opens with 'the record of the genealogy of Jesus Christ, the son of David, the son of Abraham.' Luke's genealogy comes in chapter 3.

“This is the record of the genealogy of Jesus Christ, the son of David, the son of Abraham: Abraham was the father of Isaac, Isaac the father of Jacob, and Jacob the father of Judah and his brothers.”— Matthew 1:1-2 (BSB)