Short Answer: This particular text does not relate to an individual coming into unity of faith and becoming a perfect man, but rather, to the body of Christ as a whole coming into unity of faith and becoming a perfect man. This will not be complete until all God's chosen have come in, and the completed body perfectly reflects Christ. This growth of the body of Christ continues even after one individual saint dies (e.g. it continued after Paul's death.)
Ephesians 4 opens with an exhortation to "walk in a manner worthy of your calling" and love one another. Paul then goes on to explain the unity that we have with one another in Christ:
There is one body and one Spirit, just as also you were called in one hope of your calling; one Lord, one faith, one baptism, one God and Father of all who is over all and through all and in all. (v.4-6)
Paul then proceeds to clarify that even though we are one, we each have a different function in the body of Christ:
But to each one of us grace was given according to the measure [i.e. allotment] of Christ’s gift. Therefore it says,
“When He ascended . . . He gave gifts to men.”
After a brief tangent discussing His ascension and prior descension, He comes back to the "gifts":
He gave some as apostles, and some as prophets, and some as evangelists, and some as pastors and teachers, (v.11)
Next, Paul explains the Lord's reason for giving these various gifts to men upon His departure: They were...
for the equipping of the saints for the work of service, to the building up of the body of Christ; until we all attain to the unity of the faith, and of the knowledge of the Son of God, to a mature man, to the measure of the stature which belongs to the fullness of Christ. (v.12-13)
After a brief tangent in which he urges them to therefore stop being led astray by every "wind of doctrine" he returns to his exhortation to the body of Christ:
speaking the truth in love, we are to grow up in all aspects into Him who is the head, even Christ, from whom the whole body, being fitted and held together by what every joint supplies, according to the proper working of each individual part, causes the growth of the body for the building up of itself in love. (v.15-16)
Paul wants his readers to love one another and recognize that they are one with one another in Christ; they are one body. As a result, they are each to use their individual gifts to serve the body so that the body can grow into the full image of Christ, the head.
How long will this growth take?
This growing of the body into the full stature of Christ will not be complete until the entire body of Christ is perfectly functioning together to reflect Him perfectly. (I suspect that will not happen until His return, though that is more of a theological topic.)
But I think the answer to your question is essentially that this is about the body of Christ as a whole, and not about any one individual Christian.