There is some evidence but not "pretty good" evidence. There isn't much evidence written in the time he was supposed to have been alive. Most of it was written long after the fact by 3rd parties.
The problem is that intelligent autodidacts confuse the disciplines of science (developing theories and performing experiments to provide potentially disprovable evidence of universal, timeless laws of nature) and history (the study of written texts about events that occurred in the past) and the types of evidence acceptable to both fields. Hint: they're completely different.
The problem is that, if you want to advance a historical theory claiming that there was no historical guy called Jesus who inspired the gospel, you have to come up with a compelling theory, based on historical (written records from the past) evidence describing who built the first churches, who wrote the first gospels, why they made up a story about a Palestinian Jew who was crucified 300 years ago, and why that story was so compelling it caught on with the masses and elites alike.
Or you could just go with the idea that there was a guy running around the middle east 2,000 years ago, who pissed of the Jewish and Roman elite, so much to the point that he was executed. And about whom miracles were claimed to have been performed.
The thing is, for all religions developing where we have iron-clad evidence (Mormonism, Scientology, etc), it always starts with a charismatic leader who attracts a following. Throw a rock in India, and you can find any number of gurus who are said to be capable of levitating, not eating for long periods of time, etc. etc. There is nothing really extraordinary about the story of Jesus, comparatively speaking.
If you're going to make a historical theory that Jesus never existed, but instead was invented by someone else, you have to identify that someone else. In fleshing out your theory, you'll probably want to say why they invented it, and why it caught on, when many other small cults and gurus petered out.
Christianity didn't arise out of nowhere in, say, England in 1500.
As to timeframe: A lot of key written evidence of Jesus was authored within a century of his life, which comparatively is "pretty good" as far as these things go. Much written evidence of historical events or people that we have wasn't contemporary to the subject in question either, but authored by historians, sometimes far later than a century. By that standard, the contemporaneousness is "pretty good".
As to Sources: In addition to the synoptic gospels, you also have non-Christian, non-sympathetic sources such as Tacitus referring to the Crucifixion of Jesus by Pontius Pilate. Or Josephus. This represents a variation of disconnected sources (not informed by each other), that by any standard is comparatively better than most.
So the quality of the evidence is built upon not only the _quantity_ of accounts, but the variation of sources, and the general agreement of even basic facts (existence, death). This quality is better evidence than we have of many historical figures that we assume to be real. And as another comment pointed out, the simplest explanation is that this doesn't represent a grand conspiracy of disconnected ancients.
Thats not an argument for the accuracy of the story, thats an argument against the accuracy of the rest of history.