He became the Son only at His taking on flesh.
This is not what Christianity teaches. He was God's son before He assumed a human nature. His birth to Mary did not make Him God's son. Basic stuff.
(5) We can only rightly understand the term “the only begotten” when used of the Son, in the sense of un-originated relationship. (5a) The begetting is not an event of time, however remote, but a fact irrespective of time. (5b) The Christ did not become, but necessarily and eternally is the Son. He, a Person, possesses every attribute of pure Godhood. (5c) This necessitates eternity, absolute being; in this respect He is not ‘after’ the Father;
(8) In Jn 3:16 the statement, “God so loved the world that He gave His only begotten son” must not be taken to mean that Christ became the only begotten son by incarnation. (8a) The value and greatness of the gift lay in the Sonship of Him who was given. (8b) His Sonship was not the effect of His being given. (Strong and Vine’s, 167)