Mihajlovic
Its Baltic!
Almost definitely is pushing it from what I know, it's just more than likely (as is his baptism and crucifixion). The name's been transliterated into Greek and then Latin, he'd have actually been called something more like Yeshu or Yeshua. Not much else you can get a good idea of when the next independent source to mention him is over half a century later.
You can pick and chose which evidence is credible and which not. Paul mentions Jesus in his writings and his texts are the oldest in the NT. So that's the oldest evidence. Paul has never seen Jesus personally but he was in contact with some people from the group, most notably Peter and Jesus' brother Yakov (the founder of the Jerusalem church). Those guys, and quite a large number of others, have testified to Paul what they have witnessed, and they all speak about a resurrected Jesus. The NT makes it clear that not even Jesus' brother believed who he was/ who he claimed to be during his life time but changed upon witnessing that he's alive again. After Paul's writings a few of those from the Jesus' group started writing down some material, focusing on different perspectives of Jesus' activities and addressing different audiences. That material was written a few decades after the death and resurrection of Jesus. Apart from Josephus there are no other significant, contemporary Roman sources mentioning Jesus- and why would they? Palestine at that time was full of religious teachers, religious groups, various sects. Considering Jesus spent most of his time in Galilee, he would have hardly made an impact on a Roman historian. It is only after the resurrection that this Jewish movement starts developing and growing into a bigger religious group and is then getting picked by the Roman radar.