The Bible is Christianity. The dogma surrounding the Bible can be considered "not Christianity". The Nicene Council and other Councils can be considered "not Christianity".
Seeing as certain books of the Bible were removed and others found, we don't have the complete story of Christianity. But translating 2000 year old text from a dead language to multiple languages where the authors wrote about the events after they occurred is going to create an issue of accuracy.
I wouldn't say this is exactly accurate. The Bible is the centerpiece of Christianity, the most well-verified texts we have on the faith as it existed from the beginning. But that doesn't mean it "IS" Christianity, to believe that so was a recent invention.
The most obvious proof of that is that Christianity existed long before the Bible did. Jesus's teachings were spread through word of mouth and the ministry of his disciples long before anyone wrote any of it down, because it was an era before printing press and widespread literacy where important messages were spread by people. The letter of James and the first letters from Paul were likely written about 50 A.D., still well within the ministry of Jesus's direct disciples and many other people who knew them (thus providing for reality checks), but well after the faith had already spread. Around 60 A.D., probably about the time that most of the disciples were starting to die off or get hold and the realization came that it all needed to be set down definitively in writing for the next generations, the Gospel of Mark was written, and over the next 10-20 years the Gospels of Matthew and Luke followed. Again, these would all have been written still within the lifetimes of disciples and crosschecked by eyewitnesses (as Luke himself mentions in his text), otherwise they wouldn't have been found valid by the many living followers who knew what Jesus had really done or the thousands who had heard it directly from his disciples. By 90 A.D. or so, 60 years after Jesus, the letters of John had been written along with the book of Acts chronicling the early history of the Christian community. These were probably the last books written within a timeframe where direct validation by eyewitnesses of the original events was possible, though indirect evaluation by those who were taught by the eyewitnesses was also important.
What's the point of all that? You're talking about 60 years of history of the Church where the Church spread from Galilee and Jerusalem to Ethiopia, Syria, Greece, Turkey, Rome, Egypt, and beyond....and yet the Bible STILL had not even been written yet, much less put together! Christianity existed, Christians had even been getting persecuted for decades already, and they didn't even have a book called "the Bible" yet. So how can you claim that the Bible and Christianity are synonymous.
Through the 100s you had churches all across the Middle East, North Africa, and Southern Europe that were reading from the various letters and gospel accounts in their services. They didn't have everything compiled into a single book called "the Bible", but most of them had a pretty standard list of texts that they read in order to keep the train intact. Those texts always included the four Gospels, the book of Acts, the letters of Paul, and the first letters of Peter and of John. Outside of that there were some minor discrepancies - some churches had the letter of James and others didn't, some churches had the letter to the Hebrews and others didn't, some churches read the 2nd letter of Peter and others didn't, some churches had one of the letters of John and others had all three, some churches read Revelation of John and others did not, some church read a couple additional letters like the Letter of Barnabas or an early 100s prophecy called the Shepherd of Hamas.
It was somewhere around 150 that everyone began agreeing on exactly which books were the "most appropriate" rendition of the faith. This was about the time the last "disciples of the disciples" were dying out, like
Bishop Polycarp, the famous disciple of the Apostle John who was martyred by the Roman Emperor at the age of 86 in A.D. 155. So you still have a fairly close connection to the original events, it's like now where you still have people around whose grandparents told them about fighting in World War 1, but you also are talking about 100+ years of history in-between where Christianity was able to develop based on shared teachings and discipleship and church documents like The Didache without having everything standardized into the Bible.
The center of Christianity is the life and death of Jesus Christ, his ministry and teachings and all that he did for us. Our absolute best record of that is in the Bible, and the Bible can be trusted as it was written at a time when the disciples of Jesus and their teachings were too powerful in the Church to be overcome by new and false teachings. People took word of mouth seriously back then, if 100 people witnessed an event and then each told 100 people about it, then you'd have 10,000 people who had heard about the even first-hand from a witness. And they're going to be talking. If you came in and wrote a book that contracted that, you'd be buried quick because there are 10,000 people who heard the real story first-hand from witnesses who are going to tell everyone that you're full of crap. So I believe the Bible is accurate, but I don't believe it is everything.
The ultra-focus on "the Bible is everything" didn't develop until after Islam, when Muslims were preaching "the Koran is everything" and some Christians began to adopt that mentality back in reverse from them. And then it really spread during the Protestant Reformation, which was in the age of the printing press when books became vital, and also had that Enlightenment "modern" worldview of legalism and pretending perfect knowledge even where it's impossible. It was easier for an Enlightenment-era thinker to point to "this is THE book" than to admit that they were dealing with the messier history of people and church, and so they overemphasized the book. But that's not how it was in the beginning.
