Solomon was a type of the Son of God who is King of God's people.
Begotten simply means natural son.
In 2Sa 2:5, 13-14, for the King to declare someone his "son" meant he was naming that person as a subject king over his people under the authority of himself.
That is Paul's meaning in Ac 13:33.
Jesus was declared with power to be the Son of God (King over the Father's people under the Father's authority) by
the resurrection.
If you want to think Solomon is a type of son in this regard that is up to you. But, you know that Paul is not using "begotten" to refer to natural processes. He is speaking of resurrection. This is a completely non-natural event.