Why is there no pagan historical evidence written by authors who were alive during the life of Jesus?

Documentation Evidence Any expectation of Documentation or written Evidence must take into consideration all the natural disasters and human wars that took place during the era in question. And when we look at the first century Mideast, we are confronted with both types of calamities to the max! The Mideast is known for its earthquakes. Dilapidated temples, colosseum ruins, destroyed villages dot the landscape like so many mushroom patches in a virgin forest!

In fact, remember that in 30 AD there were two Earthquakes surrounding the crucifixion and resurrection of Jesus (Matthew 27:51, 28:2). The Jewish Talmud recorded the fact that the Sanhedrin had to move to another location beyond the Temple for their meetings, 40 years before the Destruction in 70 AD: 30 AD! They considered this a bad omen.

Consider that in the Destruction of the city of Jerusalem and its Temple, which was burned and flattened to the ground, all documentation was destroyed. There were no longer any record of the Genealogies, which invalidated the lineage of the priesthood forever! Surely any reference to Jesus by the rabbinical schools would also have been wiped out.

Having noticed this, Documentation did continue to exist, written by the Apostles and disciples in the first century. No skeptic can legitimately discount this evidence of the life of Jesus. Fortunately, the Apostles had been warned by Jesus to flee Judea before the Roman invasion, so were able to keep their notes intact. (Matthew 24:15-16)

Secular Documentation Several important documents do exist, written by secular historians and government officials during the first couple centuries. Tacitus, a reliable historian (55-117), wrote in Annals, XV,44:

Consequently to get rid of the report, Nero fastened the guilt and inflicted the most exquisite tortures on a class hated for their abominations, called Christians by the populace. Christus, from whom the name had its origin, suffered the extreme penalty during the reign of Tiberius at the hands of one of our procurators, Pontius Pilate, and a most mischievous superstition, thus checked for a moment, broke out not only in Judea, the first source of the evil, but even in Rome, where all things hideous and shameful from every part of the world find their center and become popular.

Other important Greek and Roman writers and historians also documented the Life and Times of Jesus and His disciples. Pliny the Younger, governor of Bythinia (109-111) wrote to Emperor Trajan describing the Christian worship and conduct in society. (Epistles X.96)

A second century Greek satirist, Lucian of Samosata, also wrote of Christ and His disciples. Note that he is basing his info on previous generations of knowledge. So, just because he is writing later, his testimony cannot be dismissed:

(Christians) still worship the man who was crucified in Palestine because he introduced this new cult into the world...The poor wretched have convinced themselves, first and foremost, that they are going to be immortal and live for all time...Furthermore, their first Lawgiver persuaded them that they are all brothers of one another after they have transgressed once, for all by denying the Greek gods and by worshiping that crucified sophist himself and by living under his laws. (The Passing of Peregrinus, 11-13)

Beyond this, Julius Africanus quoted the historian, Thallus, concerning the darkness that accompanied the crucifixion of Jesus (Extant Writings, 18). And the Babylonian Talmud, based on the records of the Jews, alleged that Jesus was killed on "the Eve of the Passover" and that He practiced sorcery and led Israel astray. (Sanhedrin 43a)

Gospel Story Combining all the historical documentation, an honest seeker after truth can come up with the Gospel of Jesus, a real life individual who broke into human history in the first century with a Revolutionary Kingdom message of Love!

The eye-witness testimony of the Apostles is repeated in historical documentation, by men whom secularists consider reliable.

There are two major issues with finding any written evidence.

The first is that the writers would have needed to find it important enough to write about. Everything had to be handwritten, so people were not looking to write down everything.

The second is that they may have written, but the documents have not come down to us. To claim we have "a large number of documents" is an exaggeration. Papyrus was widely used to write, and it decays within a hundred years except under exceptional conditions. (Desert, for instance. Egypt has a lion's share of documents from this era, occasioning fierce historians' disputes about how typical Egypt is.) The effect was that for a few centuries after Christ, any document that no one bothered to copy was utterly lost.

As a consequence, a vast number of documents are lost to us. Many writers are only known from quotations by other writers, or even quotations of their works within quotations from other writers who are quoted by a third author.

Argument from absence is therefore very weak.