Non-Christian evidence is very thin. The most explicit statement by Josephus has almost certainly been modify by Christian editors, though most people today think there was originally some reference to Jesus. There's a second reference in Josephus that's probably original. These would point to Jesus' existence, but say virtually nothing about him except that he was called Christ. That's actually fairly significant in itself if you understand what Christ meant.
Tacitus, around 60 AD, refers to Christians and says a small amount about their beliefs. The problem is that it doesn't reflect direct knowledge about Jesus, but refers to Christian claims about Jesus. Still, it's good evidence that Jesus wasn't a myth created later, as I've sometimes heard. It's an early reference for Christian beliefs that's independent of the NT.
Beyond that, the NT and early Christian writings are about the only evidence. I think they're pretty strong. Why would anyone else have written about him? We don't have a file of birth certificates from 4 BC, so about the only documentation you can expect is people who were impressed by him.
Paul is the earliest writer, and appears to reflect traditions that were passed on to him. While Matthew, Mark, Luke and John aren't independent witnesses, they seem to reflect several different sources. So we have a number of traditions all claiming to go back to Jesus, each reflecting somewhat different understandings of him, the earliest from 30 years or so after his death (and in Paul's case reflecting older traditions). I find it hard to imagine a scenario for this that doesn't include Jesus actually existing.
The well-known atheist writer Bart Ehrman got sufficiently upset by people assuming that he thought Jesus didn't exist that he wrote a book describing what he thought we actually know about Jesus. I think some of his interpretations are based on out of date scholarship, but I agree that we have some information about his life and teachings.