Nobody knows whether anybody wrote anything about Jesus during his lifetime. If they did, we don’t have it anymore. That doesn’t mean Jesus didn’t really exist. He probably did. But everything we know about him had to pass through several people before it reached us. It’s hearsay, not eyewitness accounts.
Jesus probably was crucified about 30 AD. Josephus’ History of the Jews is the oldest piece of writing that isn’t the Bible and mentions Jesus. Josephus was born about 38 AD. So that’s probably after the Crucifixion. He published his History in 93 AD. By that time everybody who could have personally known Jesus was dead. (It’s also not clear whether he really wrote the bits about Jesus. Other people may have stuck some or all of those sentences into Josephus hundreds of years later.)
Pliny the Younger definitely wrote about Christians. He mentions Jesus in a letter to the emperor Trajan written about 112 AD. But that’s also after the death of anyone who could have personally known Jesus.
The Roman historian Tacitus wrote about Jesus in his Annals, about 116 AD. Tacitus mentions that the Emperor Nero persecuted Christians in Rome in 64 AD. But that’s not the same as a source about Jesus himself, and it’s a reference to something that happened a generation after the Crucifixion.
Another Roman historian, Suetonius, writing about 120 AD, mentions Jews who followed “Chrestus” in Rome about 50 AD, but again the events are twenty years after the Crucifixion, and Suetonius is writing almost a hundred years after the Crucifixion. The earliest pictures of Jesus that we still have today are even later, from the early 200s AD.
We do have independent knowledge of some other people mentioned in the Bible. We know from inscriptions and gravestones that Pontius Pilate and Caiaphas were real people, and there are written sources that tell us about King Herod.