It's hard to know. The first time we know of someone who's not a Christian mentioning him (probably) is the Roman historian Suetonius around the year 100, who wrote that the emperor Claudius (around the year 50) kicked the Jews out of Rome because they were causing riots "on account of Chrestus." It's not entirely clear that he's referring to Jesus, but if he is, than that would suggest that by the time Suetonius is writing, "Jesus Christ" was enough of a well-known name that Suetonius can expect his readers to know who that is. But that's at least a few decades after Jesus died. We don't have any written sources about Jesus from during his lifetime.