What Supports the Historicity of Jesus? There are several approaches to verifying the historicity of Jesus. Notice:
1. Historians There is, first of all, the Jewish General Flavius Josephus, who wrote several histories of the Jews. Some of his paragraphs are controversial, but some are definitely related to the history of events related to John the Baptist, who introduced Jesus to humanity.
Besides the renown Jewish historian, there are the secular historians which you mentioned, Pliny the Younger (correspondence with Trajan), and Tacitus (Annals, 15:44).
Suetonius, Lives of the 12 Caesars, cannot be dismissed (Claudius, cf. Acts 18:2; Nero). Without the existence of Jesus, these historical references would not make sense.
2. Other ancient References There is the writings of the Stoic philosopher, Mara Bar Sarapion. And there is the reference in the Jewish Talmud which would be meaningless without the existence of Jesus (Sanhedrin, 43a). There is also the correspondence of Abgar of Parthia and Tiberius the Emperor. Add to these the reference of Phlegon of Tralles in his histories, Africanus Chronography, 18:1.
3. Critics Indirect references are given by the early Christian Apologist to the writings of Celsus, a critic of Christianity. If there were no historical Christ, Celsus would not have endeavored to attack Christianity.
Note that we also have the speeches of the Christian apologists who had to defend their Faith in front of the Emperors, such as Justin Martyr. Their faith was in a real Resurrected Person for whom they were willing to die!
4. The Church Noteworthy in proving the historicity of Jesus is the existence of the Churches scattered throughout the Roman Empire in the first century. A Church institution without a "Founder" is most unlikely...most unreasonable...to any thoughtful researcher! Buddhism without Buddha? Islam without Mohammed? Christianity without Christ? Hardly!
Bascilicas dot the ancient Mediterranean landscape as evidence of a movement founded on the existence of a Risen Savior named Jesus. Even the underground carved out churches surrounded by the disciples's homes in Cappadocia are evidence of the movement started by One, Jesus of Nazareth.
And the enduring, persecuted Church worldwide throughout the centuries screams out, "Jesus Lived" and still lives. This is reinforced by their Testimonies of interaction with Christ in their lives! Supernatural deeds and events happening in His Name! Testimonies that cannot be explained by natural law, nor by coincidence, nor by psycho-sematic causes. No logical reasoning would attribute the Church's existence (Christianity) to a non-person.
5. Archaeology The Gospel accounts of Jesus are verified by the discoveries of the science of Archaeology. Named villages, customs, the Temple, the feasts, coins, pools, roads, coffin of the high priest, synagogues, rulers, Roman paraphernalia, laws, Jewish ritual...all the things that surrounded the life and times of Jesus are in evidence...which we would expect if a historical Jesus revealed in the Gospels really existed!
The Historicity of Jesus is not doubted by honest intellectuals and credentialed historians (who write volumes, such as H.G. Wells, Neander, Mortimer Adler, Edersheim, et al.). They all consider the evidence to be overwhelmingly in favor of the existence of a Person who has affected the life of planet Earth in a magnificent, enduring way.