Celsus, a second century author and critic of Christianity, did not make the claim that Jesus did not exist. Early Roman and Jewish critics of Christianity did not make the claim that Jesus did not exist. Instead, their claims were that he was the son of a Roman soldier (no virgin birth) and that his miracles were attributable to the same common magic that everyone believed in at that time.
If I were writing in 170 CE, and wanted to prove that Christianity was false because Jesus was made up, then I would probably say that.
Historians are aware of the fact that texts can be altered or manipulated or untrue. That’s part of the process of reading a primary source - thinking critically about what your source is saying, what biases they might have, and yes, if there were alterations or manipulations. There is ample study and linguistic analysis to determine those kinds of changes.