A difficult passage and connected with much of a controversy, for different mss say differently, some ὁς (who), some - the majority - θεός (God); the last reading is confirmed also by ancient theologians such as Ignatius of Antioch, who c. 107 AD seems to allude to the 1 Timothy 3:16 in saying in his letter to Ephesians: εις ιατρος εστιν, σαρκικος και πνευματικος, γεννητος και αγεννητος, εν σαρκι γενομενος θεος (one is the Physician, both fleshly and Spiritual, begotten and unbegotten, God who came to be in flesh (Eph. 7:2), and again: θεου ανθρωπινως φανερουμενου - "God manifested humanly" (ibid. 19:3).
The two questions should be put other way about, I guess, for first terminology and notions should be established and defined, and then the question containing those terms and notions dealt with; so first should be answered the question "what is mystery" in Pauline language.
Paul was addressing the representatives of Greco-Roman culture, and for this culture "mystery" (μυστήριον) represented an encounter with a divine, supra-human, which encounter was to change man, so that he would become an initiate. The etymology of the word is μύειν (to keep silence, keep mouth shut), which has two significances: a) it is not permissible to talk about the mystical experience (say, of Eleusinian mysteries: for instance Aeschylus was condemned to death - later to be changed by an exile - when he revealed some items of Eleusinian rituals in one of his plays) and b) it is impossible for human tongue to express the profundity of the experience.
The apostle just substitutes the Hellenic mysteries, which bore only a dim hope of eternal life (as Cicero says very vaguely: "we have learned from them the beginnings of life, and have gained the power not only to live happily, but also to die with a better hope," Cicero, Laws II, xiv, 36), with true Christian mystery of a real transfiguring touch with God and His truth, with clear and unequivocal hope of eternal life (1 Cor. 15:19-21 and in many other places). Even Paul's idiosyncratic assertion - not to be found in any other NT author - that Christians are to participate in drama of their God, in Jesus' life and death, in order to be also risen with Him (Romans 6:5), is, not to say inspired, but influenced by Hellenic attitude of an initiate participating in drama of life and death of his god, say, of Osiris or of Dionysus; in this way, one can say that Paul appreciated some value of Hellenic attitudes, stamping them into his creatively elaborated message about the one true God revealed in Jesus (on this see more in W. H. Friend's Rise of Christianity (1984) in a chapter on Paul's mission).
This mystery, this truth, for Paul, was concealed before the advent of Christ, but after His advent was revealed to His saints (Col. 1:26). And this revelation of mystery is never something communicable as an information without inner participation, but mystery is an experiential knowledge, which makes a knower an initiate, a bearer of this mystery, for the word or essence of the mystery should become an "organic", intrinsic, existential and also governing aspect of entire human life, which is finely expressed by James 1:21 as ἔμφυτον λόγος or "word implanted in us", that is to say, that word, which grows in us "organically", experientially, and transfigures us to a new creation in Christ (2 Cor. 5:17). In fact, the mystery of the new, unprecedentedly intimate knowledge of God is not something outward and just informational, but this knowledge is a mystery that works within our hearts, for God Himself works in us (1 Cor. 15:10), providing to us greater and greater entrances and knowledge of unfathomable depth of His mystery, so that different people have different levels of the initiation, some being ready for "solid food", others yet only for "milk" (1 Cor. 3:2).
So far about the meaning of mystery.
Now, what is the content of it according to 1 Timothy 3:16? What is that novelty, which made possible this unprecedentedly intimate relationship of God with His creatures? Whether you put there θεός or ὅς, the idea is the same, for if subject is θεός (which I think is the case, but I do not go now into it for this is a subject of a separate and quite interesting textological discussion/controversy), it means that Jesus is God, revealed in flesh.
However, even if it is ὁς as referring to Jesus, that means that before being revealed in flesh, in history, He was necessarily in a supra-fleshly state; and where and with whom was He? Of course with His Father, and being with Him, He was equal to Him, as asserted unequivocally by Paul (ἴσα θεῷ)(Phil. 2:6). So, "he" (if we put ὁς instead of θεός) denotes the one who is equal to God and carries the entire fullness (πᾶν τὸ πλήρωμα) of God in a bodily way (Col. 2:9). Now, the one who carries the entirety of God is necessarily Himself God, for if God is perfect, the one bearing the entirety of this perfection is equal to God and God Himself.
It is utterly unreasonable to assert that God's Son was not always and eternally so, and became perfect in some kind of a temporal process and only then through Him God created the universe (Hebrews 1:2), for then one must weave "godless myths of old wives" (1 Tim. 4:7) about some process before creation of the world, before even time, when Logos of God was growing from an imperfection and less-divinity to a perfection and full-divinity. This is an absurd supposition, for there cannot be temporal process before time. In fact, the very creation of the world is not a process but an instance that has no gradation, and only gradation can be measured by time, but creation is just positing of something that was not before and the act of positing from no-existence to yes-existene cannot be measured by time, being an instantaneous act. Therefore, if even the instance of creation cannot be measured by time, how much more the creative Principle, the Son of God, the Logos of God Who precedes this instance and who shared the identical glory with His Father before this instance (John 17:15), cannot be measured by any time and any process!
And exactly this is the mystery asserted in 1 Timothy : God has been revealed in human flesh, and "justified in Spirit", which means that this unfathomable mystery is acknowledged and made known to humans by the Spirit of God, who fathoms God (1 Cor. 2:11) and, through Whom only, we can understand that it is meet and correct to worship Jesus as Lord (1 Cor. 12:3), for this "justified" has the similar power as "I will sanctify my holy name" in Ezekiel 36:23, that is to say, He will admonish Israelites not to profane His name; and similarly here, through Holy Spirit the mystery of Incarnation of God is justified and not to be tarnished by reducing it to any lesser significance.