Your definition of documentary evidence is incorrect, at least as it relates to the study of history. When historians says that they have "documentary evidence" for an event, they mean they have some written documentation written by somebody which describes that event. In some cases, there is additional evidence, perhaps from archaeology, which supports the documentary evidence. In other cases there is nothing at all other than the documentary evidence. In such cases, they evaluate the documents to determine how reliable they are.
Consider one example. The late Carl Sagan, the world's mst famous skeptic, wrote fulsome praise for scientists from ancient ionian scientists, such as Heracletus, Anazimander, and Xenophanes. There is absolutely no evidence that these men existed other than documents about their life. Yet Sagan never doubted that they did exist. The same is true for literally thousands of historical individuals whose existence no one questions--the only evidence for their existence is documents about them. If we were to follow the standards that you apparently demand, we'd have to conclude that virtually no one in the ancient world existed.
In the case of Jesus Christ, we have four historical biographies written about him roughly 40 to 50 years after his earthly life. Those biographies are complete (most ancient documents are fragmentary), they have an exceptional level of detail and precision, and they are supported by a large body of additional information from letters written by Christ's followers and by outside historians. There are very few individuals from the ancient world for whom we have the same wealth of high-quality evidence that we have for Jesus.
Here's a better question. Do you believe that the former planet Pluto exists? How about ecosystems and deep-sea vents? Or the molten iron core of the earth? Now we, that is the people on this board, cannot experiment to verify the existence of these things, since none of us are top-tier scientists with the resources to do so. Our only options are to either believe or disbelieve what the authorities write about these things.