That seems an increasingly poor basis to build a religion, and faith upon however. You two arguments are there must be a factual evidential person upon which the biblical account of Jesus is based as the story does not make sense without one, and that lack of evidence of a something does not constitute the lack of something and that jesus was unremarkable enough to not warrant any kind documentation.

I will address your first argument with this: There are multiple authors in the Bible who address the concept of Jesus fairly distinctly. For example, the Messianic Jesus represented in the Synoptic Gospels, the Moral Jesus of the Pauline Epistles, and the Apocalyptic Jesus of Revelations. This does not seem to constitute a concrete Jesus but instead, a representation of the author's convictions, and intended message. Furthemore, there are conflict between these interpretations of Jesus such as the forgiveness doctrine and the obedience doctrine, forgiveness being almost entirely absent from Pauls letters. There are some token references in Luke-Acts, but its arguable whether Paul wrote these, or one of his adherents did, or someone else entirely.

You second argument, that absence of evidence is not evidence for absence, while technically correct can only be taken so far. Lets take two events that are in all of the gospels, the Temple Cleansing Event, and the Crucifixion Event. First the Temple Cleansing Event wherein Jesus flips tables and generally raising Cane. There are some serious issues with the description of the event: the Jewish Temple had temple guards with Centurion authority to prevent exactly this sort of thing and Jesus would have certainly been arrested for this sort of disturbance. While it is possible that Jesus' supernatural nature allowed him to do this, the Gospel authors are generally pretty good at indicating when Jesus invokes his power, and all four authors are mysteriously silent on this, and an arrest is not documented in the Gospels.

The second event, the Crucifixion Event, was not documented outside the Bible which is strange given that Roman Law required that all criminal proceedings record the accusation, and method of punishment and rerecorded in Rome's central justice building. There are interestingly no record of a person being executed for being "King of the Jews" which was the stated reason for execution in multiple gospel accounts. If there were no execution quite a lot of dogma of forgiveness falls apart, and the spectacularity of Jesus is muted.