Your answer to this question was accurate except you made the statement that God does beget and the Son was begotten. This is incorrect. The Son, as spoken in the book of John, has always existed as part of the Trinity. The word “begotten” should more accurately be translated as “unique” or “One of a kind”. I know you didn’t mean to state that Christ was begotten by the Father but you left that impression. This is the same mistake that a lot of people make, thinking Christ didn’t exist until He became flesh.
In Psalm 2:7 (KJV) God said, “Thou art my son. This day have I begotten thee.” The Hebrew word is yalad and is always used in reference to child birth. Obviously the Father was speaking prophetically to the Son in reference to Him becoming human.
The Greek word translated begotten in John 3:16 is monogenes. It appears 9 times in the Bible. Six times it’s translated only begotten, 2 times only and 1 time only child. It’s always used of children in relation to their parents.
While the Bible clearly shows Jesus to be the eternal Son of the Father, he is also the only human with a biological mother who can claim God as His father. Even Adam, who is called the Son of God in Luke 3:38, had no mother and therefore was not begotten. Thus Jesus is the only begotten son of God.