You need to first know what the nature of history is. Here is a quote from Jewish historian Josephus (lived 2000 years ago).
The Wars of the Jews, book 2, chapter 12, section 8
After this Caesar sent Felix, the brother of Pallas, to be procurator of Galilee, and Samaria, and Perea, and removed Agrippa from Chalcis unto a greater kingdom; for he gave him the tetrarchy which had belonged to Philip, which contained Batanae, Trachonitis, and Gaulonitis: he added to it the kingdom of Lysanias, and that province [Abilene] which Varus had governed. But Claudius himself, when he had administered the government thirteen years, eight months, and twenty days, died, and left Nero to be his successor in the empire, whom he had adopted by his Wife Agrippina's delusions, in order to be his successor, although he had a son of his own, whose name was Britannicus, by Messalina his former wife, and a daughter whose name was Octavia, whom he had married to Nero; he had also another daughter by Petina, whose name was Antonia.
I want you to take a look at the last name appeared. By applying the line of reasoning in OP, Antonia can't exist!
That could be a nobody's name possibly mentioned only once in a history book. How will you evaluation whether the author is a "qualified investigator" of Antonia in this case? There could be no where says that Josephus actually knew Antonia, or how credible his investigation was in this specific case regarding to this nobody figure Antonia.
This "Antonia" case however is almost typical of what history is. The author believed that the information should be for credible accounts (ultimately eyewitness accounts), then he will or can include "Antonia" in the book of history without actually knowing her personally. That's how history "works".
If you have question the "qualification" of the author or evidence of Antonia's existence, well you may have tick her out of the book (i.e, by following the line of logic in OP).
History is the recording of 0.00000000000000000000000000000001% of human activities of 0.00000000000000000000000000000001% humans who happened to be known of by a historian. Antonia is rather a side figure (unimportant), most history are about famous person who had influence to the society where an author ever lived. Sometimes we have no choice but to count in what was said as "what could possibly happened" even in the case of famous persons and events, not to speak those nobodies such as Antonia.
On the other hand, "influential figures or events" are almost exclusively in a secular sense. Jesus is just one of many self claimed Messiah ever existed. No one back knew Jesus would have an influence to today's world. It's almost natural that an author living in Jesus' time would take all the self-claimed Messiah equally, and to exclude them from a serious history book. Even when Jesus was seriously recorded down by secular means (to be more specific by the Jewish means), the writings may not have a chance to survive the AD 70 siege. How many Sanhedrin writings and books still exist today? It's almost none. Today's Jewish teachings are mostly based on authors living after AD 250.
In a nutshell, with that 0.<xxx>1% out of 0.<xxx>1% human activities recorded in our history, minus those you can't make the author "qualified" or the activities evident (oh no, most of them can't be evident if you'd like to count history books on a page by page basis), and then come to the conclusion that the 9999999999999999999999999999.99% activities can't exist. Now what's that?
Like I said somewhere else, we can't even confirm recent history such as Nanjing Massacre occurred in World War II, which could possibly involve 300,000 human lives (as claimed by the Chinese). Here we are talking about a human mass activity, not to mention individual activities by the nobodies ever lived. Of course by applying the line of reasoning in OP, the Japanese must be justified to conclude that "Nanjing massacre never happened".
That being said. There's another dilemma here.
By the assumption that God exists, if He has a will to hide the evidence from humans,
in this case if He fails He's not God. If He succeeds humans thus have no evidence!
It is said that the Christian God has a good reason to hide the evidence, as if He's made evident than no humans can be saved, as humans will have to rely on faith to be saved in accordance to the current covenant in place.
So if God is true, do you want God makes Him evident such that all mankind is deemed not savable?