No, Solomon was not a type of the Son of God except in the fact that he built the house of God, not as one begotten of God.
Solomon was a figure of the subject King (
Jesus, 1Co 15:28).
Solomon was not the begotten of God, he was begotten of exclusively human parents.
Since Paul exclusively links Psa 2:7 to resurrection then
Solomon cannot serve as a type in this regard because he is still dead and his body is still in the grave.
All the types are dead, only the anti-types are not dead.
God calls Solomon his son and repeats that he is Solomon's father (2Sa 7:5, 13-14),
(which figurative, not literal language in the ancient near East meant
Solomon was a subject king under God, the King)
a figure of Jesus, son of the King (the Father) who will rule God's Kingdom
under the Father's authority (1Co 15:28) when Jesus, the subject King
has put all enemies under his feet and delivers the Kingdom over to the Father (1Co 15:24-28).
2Sa 7:13-14 is not saying that Solomon was a natural son of God,
but that
Solomon was a subject king ruling by the authority of God the King,
whose throne would be established forever (all of which which is a type of Christ,
as is the Davidic covenant).
The NT links both Ps 2:7 and 2Sa 7:13-14 to Jesus as:
the Son of God,
who is subject king ruling the Kingdom under the authority of the greater King (the Father),
and then Ro 1:4 states he was
declared with power to be the Son of God, and subject king (1Co 15:28),
by the resurrection.
The only two characters of the OT who are spoken as represent Jesus as the Son of God
was Adam and Isaac and Issac only represents him as sacrifice.
However, as you know, the OT is strewn with types of Jesus as different things; e.g.,
the Passover
lamb,
the sin s
acrifice,
David, the
king whose throne is established forever ,
Melchizedek, the
eternal high priest,
Moses, the
Mediator and
Prophet,
the show
bread in the Holy Place,
the
rock in the wildnerness,
the
manna from heaven,
the
Branch,
Solomon, the
Son and
subject king of the King, etc.
I find the meaning of Ac 13:33; Ro 1:4; 1Co 15:24-28 to be clear that
Jesus is the fulfillment of the promises to the Fathers in 2Sa 7:5, 13-14 and Ps 2:7;
that God's Son would be ruler of the Kingdom and subject king of the Father,w
which has been declared with power by the resurrection.