You have incorrectly interpreted the text. Solomon is not God's begotten son (offspring, or naturally begotten). In fact, he can't be. John 3:16, in the King James Version of the bible, says "For God so loved the world that he gave his one and only Son, that whoever believes in him shall not perish but have eternal life." (John 3:16)
What the verse you are quoting actually means is that Solomon would be loved by God as if he were His son. This is evident within the context of the message of God's word. For we are all God's creation ( Colossians 1:16 ), and those who are baptised (or "born again") are all accepted as God's children ( John 1:12 ; 11:52 ; Romans 8:16; 1 John 3:1-10 ).
Jesus is the only way to salvation because he is the only true son of God. Solomon is nothing more than a man, who has no salvation to offer ( Romans 6:23 ).