I don't have to preface this one, my answer is based on Orthodox perspective and with reaching into orthodox sources, as well as scripture of course.
It really depends on what you meant by "Knowledge of God" for me to answer, but I will attempt to answer the multiple variations that I see.
There is of course physical knowing and spiritual knowing, as well as proper "knowing" of God.
I have not seen any conflict between the Holy Spirit and the Son both being sources of knowledge about the Father.
I will not get into detail about the "filioque" and the nature of the Trinity, that would be another full answer in and of itself. The simplest response is that the filioque rotates the "triangle" of the Trinity in a way that is wrong.
Getting back to the question... :)
Referring to more "empirical" evidences and knowledge
- First, we can know Him through His Creation: Ourselves, nature, and all of creation. These things we can observe.
“For since the creation of the world, His invisible attributes are clearly seen, being understood by the things that are made, even His eternal power and Godhead” (Rom. 1:20)
“The heavens declare the glory of God;
the skies proclaim the work of his hands.
Day after day they pour forth speech;
night after night they display knowledge.
There is no speech or language
where their voice is not heard.
Their voice goes out into all the earth,
their words to the ends of the world.” (Psalm 19:1-4)
“But ask the animals, and they will teach you,
or the birds in the sky, and they will tell you;
or speak to the earth, and it will teach you,
or let the fish in the sea inform you.
Which of all these does not know
that the hand of the Lord has done this? In his hand is the life of every creature
and the breath of all mankind. (Job 12:7-10)
Other verses include... Psalm 8:1; 50:6; 66:4; 89:5; All of Psalm 148;
So we can observe many things, for example the sheer vastness of life of all forms, especially our own, and all its dimensions: Physical, mental, social, spiritual, emotional, etc. We see this directly in how intricate, beautiful and wonderful the world itself actually is. Everything from how a mother looks at her baby to the elegance of theoretical mathematics.
This means that God has provided for us, plainly, before our eyes, evidence that we need in order to believe that He is the divine Creator of this universe. He has left enough evidence of His divine nature for us to see, if only we care to take a moment to look at His creation, and if only we would take that next step of faith to believe in what it points to. As the Bible says:
“By faith, we understand that the universe was formed at God’s command”. (Hebrews 11:3)
- Second, God has revealed himself to us directly through the Incarnation of the Son of God.
Of the Godhead itself, we can also see many things. The most obvious being the evidence of all three in a historical sense. The Gospels can be viewed as eyewitness accounts (collection of eyewitness accounts if the author was not present) of historical events, of course within the Gospels we see much evidence of Christ, the Holy Spirit is seen during pentecost and the baptism, the Father is seen during the transfiguration and heard during the baptism as well.
Spiritual knowledge, or personal knowledge of God.
In contrast to the above, we realize that God is not physical (Other then the incarnation), not a mental concept and not something we can construct by philosophical reasoning.
We begin by confessing our ignorance about the essence of God.
St. Cyril of Jerusalem (315 - 386) tells us, “We explain not what God is, but candidly confess that we have no exact knowledge concerning Him. For in what concerns God, to confess our ignorance is the best knowledge.”
We cannot think of God in terms of a philosophy. Words cannot define God. Why is this?
Because, this would limit God to our own limited ability to reason. We are less than God, we are created by Him. The Creator must be larger than the created. God is infinite and beyond all finite human reason.
God in His essence is by our limited nature incomprehensible to us. We have only "some" knowledge of what He has revealed of Himself to us. But this knowledge is incomplete.
"...Unapproachable light, whom no man has seen or can see..." (1 Timothy 6:16)
“For now we see in a mirror, dimly, and I know in part” (1 Cor. 13:12)
About all we can say about God is that He isn’t this, but also, He isn’t that either. This is known as “apophatic theology” where we define God by what we know He is not. We can set boundaries that help us to know God, but never totally describe Him. We can say that God is not physically visible or is not a creation. The key is that we must be careful not to use our reason to derive a definition of God beyond what has been revealed to us through Scripture and Tradition or our direct experience of Him. (Doing so would end up being only our own mental creation of god and not God Himself).
It is necessary to go beyond words and reason to understand the true nature of the Divine.
"If you wish to speak or hear about God, renounce your own body, renounce your bodily senses, pass over the seasons of the year, their orderly arrangements, the adornments of the earth; stand above the ether, traverse the stars, their splendor, grandeur, the profit which they provide for the whole world, their good order, brightness, arrangement, movement, and the bond or distance between them. Having passed through all this in your mind, go about heaven and, standing above it, with your thought alone, observe the beauties which are there: the armies of angels, which are above the heavens, the chiefs of the archangels, the glory of the Dominions, the presiding of the Thrones, the Powers, Principalities, Authorities. Having gone past all this and left below the whole of creation in your thoughts, raising your mind beyond the boundaries of it, present to your mind the essence of God, unmoving, unchanging, unalterable, dispassionate, simple, incomplex, indivisible, unapproachable light, unutterable power, infinite magnitude, resplendent glory, most desired goodness, immeasurable beauty that powerfully strikes the wounded soul, but cannot worthily be depicted in words.” (Saint Basil the Great, Homily "on Faith", Fide 1)
The starting point to knowing God is to accept that we are not searching for a definition that can be put into words, but a relationship with Him.
This is clearly seen in things like the Nicene Creed which starts with the words "I believe", this is based on faith and not rational grounds. There are no proofs based on a logical examination of facts. It is an inner conviction with a moral foundation.
Faith is the substance of things hoped for, the evidence of things not seen (Heb 11:1)
To believe in God means that we acknowledge God with our minds and that we strive towards Him with our hearts. As an Orthodox Christians I believe in that which is inaccessible to our outward experience, such as knowledge gained through scientific exploration or what is observed by us through our senses. Those things are interesting, "cool", and of intellectual interest, but are ultimately secondary and inferior to a proper "knowing" of God.
Properly knowing God.
Knowing God is something that we cannot do on our own, because our minds are clouded by all the activities and assumptions of our current culture, regardless of which age we live in there is always a worldly influence that denies or twists our understanding of God. This means we can easily make up theories based on assumptions buried deep in our subconscious mind. We must be aware that our mind can easily deceive us and even lead us into believing that there is no God. We need to be very careful. This does not mean that we don’t use our minds to know God, but we must have caution and seek proper guidance.
To know God as best we can, we need to follow the guidance of those who have purified their minds through an exemplary Christian life allowing themselves to become capable of contemplating the exalted truths.
In the Book of Matthew Jesus tells us, Blessed are the pure in heart; for they shall see God. (Matt. 5:8)
These people are often referred to as "Saints" in modern conversations. Our Holy Church Fathers were supreme examples of such a type of person, but there are modern examples as well. The Saints start with the Theotokos (the first Christian) and even today there are people alive who will likely be acknowledged as Saints after they are no longer with us.
(This is slightly off topic, but important here. It must be stated that the only true "saint" or holy one (Hagios) is God Himself. The Bible states "For I am the Lord your God; you shall name yourselves holy and keep yourselves holy, because I am holy ... " (Levit. 11:44; 19:2 and 20:7). Man becomes holy and "sainted" by participation in the holiness of God.)
The subject of the saints is another matter, but we refer to them for guidance. It is wise to respect and be lead towards God by others who have had a deeper relationship with Him. This is why our fundamental understanding of our Faith is guided by the "Church" itself, all of the traditions of the church include those of the Church Fathers and saints, as well as the scriptures themselves.
Short answer: "Can knowledge of God can come apart from the Son?" Yes
Yes, it happens often and must be tested against Scripture and Tradition.
- Physical knowing is observed from all of Creation.
- Spiritual knowing is "through a mirror darkly"
- We acknowledge evidence through the understandings of Saints (Holy Spirit)
- We see directly through Christ, knowledge of the Father. (Son)
- However the proper "knowing" is actually admitting that you don't know God, and that you want a relationship with God, The Church is necessary for this to guide us away from sinful misunderstandings.
I'm sure something is missing, there usually is. If needed things will be edited.
Edit: Of course I didn't even get into the Sacraments, which also guide us towards knowing God as well as another form that the Holy Spirit gives us knowledge of God. Again, another whole topic in and of itself.
Peace be with you