Romans 1:3–4 was the earliest written document stating that Jesus was the son of David — just over 20 years after Jesus’ death. He is also called son of David in the gospels, the book of Acts, and Revelation.
Evidence of any serious debate in the first century — that Jesus was not from the line of David — is lacking. For example, Matthew’s gospel is unconcerned that the genealogy of Jesus is traced through the line of Joseph (his ‘adopted’ father).