The New Testament was not written in a vacuum, but written to very religious communities, created and maintained through oral tradition and the written word. While not every document used by these communities is considered canonical today by either Judaism or Christianity, they came close to canonical for these communities. We know of the long struggles over Sirach and Enoch, but nothing significant is mentioned of the Psalms of Solomon, not until the 4th century when we find it attached to a historical manuscript. We know that the PssSol is of more ancient origin than that manuscript, finding traces of it in other documents, sometimes confused with the Odes of Solomon. It is a distinctly Jewish work, and belongs squarely in the Pharisaical tradition. Further, it lays in the same genre of hope as Wisdom and other 2nd Temple Jewish documents of the Messiah and the Resurrection.
Using historical criticism, we can see a move of the heart of some of the Jewish people to a Messiah figure sent from God, to rule over an age of security and reestablishment of Israel. We can see also that they viewed the resurrection at the day of Visitation as a type of vindication against the enemies who have killed them. We can find phrases, typos, and allusions of the PssSol not in the Gospels but carrying over into John’s Apocalypse as well. If we find that the Gospels were written in a manner to type Jesus against not only the Hebrew Scriptures (as of yet uncanonized by his time) then we must begin to include sources such as the Psalms of Solomon as well.
Biblically speaking, we find that the same sect of Jews which produced Paul, and so heavily influenced the language of the New Testament, began to yearn for a hope of God in the form of an individual who would restore the righteous, chastening them, and preparing them for the Resurrection. In the PssSol we find that the Resurrection takes on a form of vindication, in which while the righteous are slaughtered their enemies rejoice, but in the end it is the righteous who will reign. In sources such as these Psalms, we find a hope for a return to pious living allowing for the reign of a Messiah with God as his King. We also find a Messiah King who does not come as a warrior might, with horse and sword, but by the power of God, vanquishing his enemies with the word (logos) of his mouth.
We can see the Messiah of the New Testament in these Psalms, and I am reminded of a passage from the Gospel of Luke:
Then he opened their minds to understand the scriptures,
Now He said to them, “These are My words which I spoke to you while I was still with you, that all things which are written about Me in the Law of Moses and the Prophets and the Psalms must be fulfilled.” Then He opened their minds to understand the Scriptures, and He said to them, “Thus it is written, that the Christ would suffer and rise again from the dead the third day, and that repentance for forgiveness of sins would be proclaimed in His name to all the nations, beginning from Jerusalem. (Luk 24:44-47 NAS)
Christ opened the eyes of the travelers concerning the Law, the Prophets, and the Psalms, but then He pointed to two prophecies,
that the Christ would suffer and rise again from the dead the third day
that repentance for forgiveness of sins would be proclaimed in His name to all the nations, beginning from Jerusalem
While commentators seek to see these prophecies as corporate, comprising the entire of the Hebrew canon (again, at this point, fluid to some extent), that might be an injustice to the text itself. We know that several books in the Hebrew bible used sources long since lost to us, and yet, we somehow deny them consideration. Are we doing the same thing there? Cannot such sources as the Psalms of Solomon actually be in the mind of the Messiah?