The Sudarium has been in Oviedo since the eighth century and likely dates to the first century. The similarities to fabrics from Masada, that suggest the linen is a linen from the first century. The overwhelming evidence that the Shroud was a source for depictions of Jesus as early as the sixth century. Historical evidence that the Shroud is the same as the Edessa Image which dates to at least the sixth century. Contrary to much public opinion, carbon 14 dating is not an exact science.
People sometimes have the idea that carbon dating is the definitive test.
Nothing could be further from the truth. Archaeologists who make use of carbon 14 studies in their research know that samples occasionally give aberrant results. Carbon dating is regarded as one tool among many. If it disagrees with the preponderance of evidence, the carbon dating result is the one that routinely is assumed likely to be in error, not the other way around. But this is not what happened with the carbon dating of the Shroud.