For example, many of Plato's (Socrates') works were mentioned by name by his students and contemporaries.
These claims have long been challenged by scholars, primarily because John Mark was a known Jew.
Setting "tradition" aside, modern linguistic scholarship on the Gospel actually suggests that Mark has two sources/authors, one dating from the 60s, and a second, possibly an editor, dating from the 80s or 90s It should be noted that one passage often cited as being added is the passage about Jesus' resurrection (Mark 16:1-8), suggesting that the original author of Mark may have been part of a church that had not yet invented the Resurrection Story.
The dating of Acts is similarly vague, with its traditional dating of 80-90 CE being some time after Paul was dead and gone, and there are some who suggest the Luke-Acts we have was in response to Marcion of Sinope's teaching, meaning neither can be earlier then 120 CE.
Ignatius of Antioch (98 CE) does not mention any of the four Gospels, nor the Didache nor Clement.
Moreover neither Paleographic or Carbon-14 is precise enough to demonstrate that there are any fragments before our earliest references to the Gospels.