In Matthew, as the King, He has a lineage (Joseph's). In Luke as a man, He has a lineage (Mary's). In Mark, there is no lineage for servants rely on none. In John there is no lineage for God has no lineage.
As heir to the throne of David, He is the "Son of David". As eternal God, He is called "Son of God". We do not, however, make the truth of His full deity and eternal Godhood require us to conclude that David is God. David is in his human lineage, as God He has no lineage.
Jesus is the Son of God
Jesus is the son of David
Jesus is the son of Man
But that does not mean that we conclude that God is a man named David. It is explained by the two distinct natures of Christ.
He is only referred to once as "son of Mary" and that by the Pharisees (who also call Him "the carpenter's son"). Scripture never refers to Mary as "the Mother of God." (only as "the mother of Jesus"). Even the catechism notes that that doctrine developed over time. It is absolutely nowhere found in any of Paul's treatments of the gospel (which he, Paul, declared as complete, never to be added to or changed).
As the Council of Ephesus stated (for what it's worth): Jesus was one person in two distinct and inseparable natures: divine and human. But that does not preclude the scriptural fact the human flesh Jesus took upon Himself was "prepared" for Him. His flesh was not eternal. He did not pre-exist as a human. He was, is, and ever shall be eternal God. His flesh which He took upon Himself was "prepared" by the Father and had a beginning. His flesh had its beginning in Mary, his deity pre-existed all things.
He was sent in the "likeness of sinful flesh." He did not pre-exist in such a likeness:
Romans 8:3
For what the law could not do, in that it was weak through the flesh, God sending his own Son in the likeness of sinful flesh, and for sin, condemned sin in the flesh:
Nestorius, in addition to rightly denying the title "Mother of God" also separated Jesus' deity from his atonement. One can agree with him (them, they still exist in the Middle east) on the first point, yet reject the second... which Baptists reject and have rejected historically. The two are concepts are independent.
In Micah 5:2 the babe is said to be "of old, from everlasting" and in Isaiah He is "the Mighty God, the Everlasting Father."
So, shocking as it may be, Baptists are Trinitarians who hold to Jesus as fully God and fully man. Hope this helps explain Baptist theology for you. Thanks for asking!