Remember the adage: "Greek gives us the range of possibilities; context makes the determination."
Maybe "adage" is too strong, since I made it up; but I do say it a lot.
Matthew starts his gospel as such: "This is the genealogya of Jesus the Messiahb the son of David,a the son of Abraham" (NIV). There is a footnote on "genealogy" that says, "Or is an account of the origin."
γένεσις has four basic meanings according to BDAG.
- "An account of someone’s life, history, life"
- "Lineage, family line"
According to Carson, this gives us three possibilities in Matthew 1:1.