Good question, "Abiblestudent", and thank you for this.
A great article I have found to be helpful over the past 10 years or so is Jim Walker's "Did a Historical Jesus Exist?", (pasted below)
Here is an excerpt from that article....
WHAT ABOUT WRITINGS DURING THE LIFE OF JESUS?
What appears most revealing of all, comes not from what people later wrote about Jesus but what people did not write about him. Consider that not a single historian, philosopher, scribe or follower who lived before or during the alleged time of Jesus ever mentions him!
If, indeed, the Gospels portray a historical look at the life of Jesus, then the one feature that stands out prominently within the stories shows that people claimed to know Jesus far and wide, not only by a great multitude of followers but by the great priests, the Roman governor Pilate, and Herod who claims that he had heard "of the fame of Jesus" (Matt 14:1)". One need only read Matt: 4:25 where it claims that "there followed him [Jesus] great multitudes of people from Galilee, and from Decapolis, and from Jerusalem, and from Judea, and from beyond Jordan." The gospels mention, countless times, the great multitude that followed Jesus and crowds of people who congregated to hear him. So crowded had some of these gatherings grown, that Luke 12:1 alleges that an "innumerable multitude of people... trode one upon another." Luke 5:15 says that there grew "a fame abroad of him: and great multitudes came together to hear..." The persecution of Jesus in Jerusalem drew so much attention that all the chief priests and scribes, including the high priest Caiaphas, not only knew about him but helped in his alleged crucifixion. (see Matt 21:15-23, 26:3, Luke 19:47, 23:13). The multitude of people thought of Jesus, not only as a teacher and a miracle healer, but a prophet (see Matt:14:5).
So here we have the gospels portraying Jesus as famous far and wide, a prophet and healer, with great multitudes of people who knew about him, including the greatest Jewish high priests and the Roman authorities of the area, and not one person records his existence during his lifetime? If the poor, the rich, the rulers, the highest priests, and the scribes knew about Jesus, who would not have heard of him?
Then we have a particular astronomical event that would have attracted the attention of anyone interested in the "heavens." According to Luke 23:44-45, there occurred "about the sixth hour, and there was darkness over all the earth until the ninth hour, and the sun was darkened, and the veil of the temple was rent in the midst." Yet not a single mention of such a three hour ecliptic event got recorded by anyone, including the astronomers and astrologers, anywhere in the world, including Pliny the Elder and Seneca who both recorded eclipses from other dates. Note also that, for obvious reasons, solar eclipses can't occur during a full moon (passovers always occur during full moons), Nor does a single contemporary person write about the earthquake described in Matthew 27:51-54 where the earth shook, rocks ripped apart (rent), and graves opened.
Matthew 2 describes Herod and all of Jerusalem as troubled by the worship of the infant Jesus. Herod then had all of the children of Bethlehem slain. If such extraordinary infanticides of this magnitude had occurred, why didn't anyone write about it?
Some apologists attempt to dig themselves out of this problem by claiming that there lived no capable historians during that period, or due to the lack of education of the people with a writing capacity, or even sillier, the scarcity of paper gave reason why no one recorded their "savior." But the area in and surrounding Jerusalem served, in fact, as the center of education and record keeping for the Jewish people. The Romans, of course, also kept many records. Moreover, the gospels mention scribes many times, not only as followers of Jesus but the scribes connected with the high priests. And as for historians, there lived plenty at the time who had the capacity and capability to record, not only insignificant gossip, but significant events, especially from a religious sect who drew so much popular attention through an allegedly famous and infamous Jesus.
Take, for example, the works of Philo Judaeus who's birth occurred in 20 B.C.E. and died 50 C.E. He lived as the greatest Jewish-Hellenistic philosopher and historian of the time and lived in the area of Jerusalem during the alleged life of Jesus. He wrote detailed accounts of the Jewish events that occurred in the surrounding area. Yet not once, in all of his volumes of writings, do we read a single account of a Jesus "the Christ." Nor do we find any mention of Jesus in Seneca's (4? B.C.E. - 65 C.E.) writings, nor from the historian Pliny the Elder (23? - 79 C.E.).
If, indeed, such a well known Jesus existed, as the gospels allege, does any reader here think it reasonable that, at the very least, the fame of Jesus would not have reached the ears of one of these men?
Amazingly, we have not one Jewish, Greek, or Roman writer, even those who lived in the Middle East, much less anywhere else on the earth, who ever mention him during his supposed life time. This appears quite extraordinary, and you will find few Christian apologists who dare mention this embarrassing fact.
To illustrate this extraordinary absence of Jesus Christ literature, just imagine going through nineteenth century literature looking for an Abraham Lincoln but unable to find a single mention of him in any writing on earth until the 20th century. Yet straight-faced Christian apologists and historians want you to buy a factual Jesus out of a dearth void of evidence, and rely on nothing but hearsay written well after his purported life. Considering that most Christians believe that Jesus lived as God on earth, the Almighty gives an embarrassing example for explaining his existence. You'd think a Creator might at least have the ability to bark up some good solid evidence.