The Apostolic Fathers is a special group of church fathers who personally knew or taught by the apostles. Some of their writings were even considered to be included in the canon although ultimately they were not. In a way they are like the 2nd generation apostles who can give us some clues on the 1st generation apostles's understanding and teaching.
The purpose of this question is to trace the development of the early church teachings about Christ between the New Testament books and the Christological formulations in the Nicene creed (as the 2nd person of the Trinity) and the Chalcedonian definition (the double nature of Jesus as fully God and fully human).
What we can learn from the answer is whether the Trinitarian and Chalcedonian formulas about Christ organically developed from the apostles's understanding of the divinity of Jesus, which were not fully explicit in the New Testament. Even so, we can already see the hints of the doctrines from the NT books (for example, see this answer for 2 resources discussing it).
Among the proponents of sola scriptura, it is commonly established that more precise formulation was motivated to combat heresies (such as Docetism, Gnosticism, Modalism, Arianism, etc.), but the generations after the apostles did NOT introduce new elements into the final formulation. In other words, those post apostolic generations made use of Greek philosophical terms and EXTENDED the meanings of those terms to make the council formulas (because the reality of Christological revelation pushed the limits of available language and concepts to describe it faithfully). Sola Scriptura proponents reject the reverse: that the church fathers introduced foreign Greek philosophical teachings into the formulas. Examining the Apostolic Fathers's writings can potentially make this case.
Accepted answer should include quotes from their writings and a brief analysis showing the continuity (if exists) between the NT books and the 2 council documents. We can then see the nature of this continuity, whether foreign Greek philosophical elements have smuggled themselves into the formulas.