Though the four Gospels were written after Paul, even early date estimates for the Synoptics would place their composition near the end of Paul's life in the mid-late 60's. Whereas the bulk of Paul's letters were written in the 50's and 60's.
There probably were proto-Gospels already extent, ancient tradition attributed to Papias speaks of an Aramaic composition of Jesus' teachings (which is oddly consistent with the Q-Hypothesis). At the very least statements such as found in 1 Corinthians 15:3-8 point to a well established tradition among the churches. Paul almost never provides biographical details about Jesus, instead writes assuming his audience knows all this.
There is an interdependent relationship between the Gospels and both the Pauline and General Epistles that expresses and resonates the life and faith of the first Christian communities.
So Jesus' words do not originate from the Gospels, but rather the Gospels bring us back to Jesus' words--words, teachings, sayings, and the things He did being part of the living and common memory of the Church. That arose into the Synoptic Gospel tradition, the Johanine Gospel tradition, the Pauline Epistles, and the General Epistles.
The New Testament is the product of a living, thriving network of Christian communities that originated from Jerusalem by the mission and ministries of the Apostles.
So to suggest that these early communities had a reductionist doctrine is misleading at best; though it would be accurate to say that the doctrinal language of the Church wrestling with the concrete happenings involving Jesus, and the work of the Spirit in the apostolic ministry are given in the New Testament writings and in the continued conversation and debates of the Christian Church.
There was a living, breathing Christianity before any of the New Testament was written, and there continued to be a living, breathing Christianity after; and the New Testament is a profound snapshot of that early period. Even more than that, these writings were found to be so important, and so vital that these communities of Christians copied them and sent them to one another, and began to incorporate them into their liturgies. That's what the New Testament is.
-CryptoLutheran