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noma
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Scriptures already existed, though not including the New Testament. These were accepted to be inerrant. How did we know which scriptures should be considered so and which scriptures not? Faith.How do we know these scriptures are infallible? Jesus did not write them. Did Christ ever say that infallible scriptures would be written?
How do we know now that we have scripture? Faith.
Like all faith, this can be tested, using nature (Scripture has no scientific errors) or using reason (Scripture does not contradict itself).
But ultimately holding to the inerrancy of Scripture is like holding that 1+1=2. It is not by the authority of the teacher. It is not because we can prove it beyond doubt. It is because of faith.