The first part of the Bible was already compiled before Constantine was born. At the time Jesus was physically on earth, there was already the part of the Bible that was in scrolls.
There was a time Jesus read a part of this scroll in the synagogue. This is in Lk. 4:16-20. You notice that after reading, he gave back the scroll to the minister incharge.
It's erroneous to claim that Constantine compiled the Bible which was already compiled before him.
In Lk. 1:1-3, we see that Luke, a physician was among those that compiled a part of the new testament. It's obvious that there were Christians who were compiling the Bible long before Constantine was born.