No I do not have it backwards. Believing precedes being born of God. John 1:12-13, ". . . to become the sons of God,
even to them that believe on his name:
Who were born, not of blood, nor of the will of the flesh, nor of the will of man, but of God."
Mark 16:16, ". . . He that believeth and is baptized shall be saved; . . ."
Acts of the Apostles 16:31, ". . . Believe on the Lord Jesus Christ, and thou shalt be saved, . . ."
Ephesians 2:8, " For by grace are ye saved through faith; . . ."
Romans 1:16, ". . . the gospel of Christ: for it is the power of God unto salvation to every one that believeth; . . ."