I am sorry to disagree with you, but attempting to prove the definition of being a Christian is believing in the Trinity is not found in the Bible. It is simply not there unless you stretch the meaning and words of Jesus. At no time did Jesus qualify his words; believe on me, repent, and be baptized and you will be saved. The most you can prove by scripture is if someone believes that Jesus was the Son of God, the Holy Savior and Redeemer of the world, was crucified to atone for the sins of the world, rose again on the third day to sit on the right hand of the Father, and will return again one day, that individual is a follower of Jesus.
The formal doctrine of the Trinity came later; it became the official doctrine of all Christianity in 325. The Church purified itself with the Council of Nicea by purging all conflicting doctrine that was being preached within itself by then. Until that time, there were conflicting teachings that needed to be set right. Unfortunately, we did not start out with a Magisterium that could maintain pure doctrine from the beginning. Even in our own day we see those who kick against the pricks, reject the authority of the Pope and begin to create false teachings.