Are we accepting, at the very least, the three Synoptic Gospels as evidence for the existence of Jesus?
If yes, then that alone should suffice--this does not necessitate that every detail in the Gospels must be accepted as historical fact, only that the Gospels present evidence for Jesus' historical existence.
If no, then then can we accept the undisputed Pauline literature as evidence? The undisputed Pauline epistles being as follows: Romans, 1 & 2 Corinthians, Galatians, Philippians, 1 Thessalonians, and Philemon.
If yes, then I would explicitly point to what Paul writes in 1 Corinthians 15, about what he had received and what he himself taught about Jesus; ergo that Paul's teaching was the accepted teaching of the earliest Christians and such involved, most certainly, an historical Jesus. And in case this should be skewed in such a fashion as to argue merely a "mystical Jesus" of a Docetic or quasi-Docetic variety we also ought to accept the statement in Galatians of Jesus having been born "born of a woman, born under the Law". Such that for Paul Jesus was indeed a real human person who was born, lived, taught, was crucified, buried, and was raised up bodily from the dead, and ascended to sit at the right hand of God. This Paul believed, and is the earliest example of what Christians believe with zero evidence of an alternative belief.
If none of this is sufficient as evidence for an historical Jesus, then I doubt any other evidence would suffice; such as the remarks by Tacitus, nor the highly contentious statements of Josephus.
I would also contend that if such is not sufficient to demonstrate an historical Jesus, then we begin to seriously put into doubt the entire discipline of historiography.
-CryptoLutheran