Mark Shea is pretty certain in an article simply called The Shroud of Turin that appears in the National Catholic Register:
Turns out the Shroud of Turin does date from the first century after all. That’s because it is, as I have always thought, the burial shroud of Jesus of Nazareth. Unless, of course, you seriously believe that a medieval European forger just happened to have a 1300-year-old burial shroud (that originated in the Holy Land) laying around and decided to use it to conduct an absolutely unique and unrepeatable experiment in photo-realistic imaging on cloth.
Mark links to a story in the Vatican Insider which boldly says that in the lede. But it doesn’t say that in the article. It is a stretch. Better to say that Fanti thinks it could be first century. He continues:
At present, however, all the evidence we have accumulated keeps pointing–with a persistence galling to dogmatic materialists–to the image being what Christians have always taken it for: an "image not made by hands" that was somehow imprinted on the burial shroud of Jesus Christ. It is not "proof" of the Resurrection. Nor is it "scientific proof" of a miracle. Science leaves off where miracles begin and the most the sciences can do is what they are currently doing: say, "We can’t explain how this image was created." But for those who have placed their faith in Jesus Christ as Son of God and his Resurrection from the dead as their salvation, the Shroud is a particularly striking witness, as are the various other signs and wonders God has done down through the ages. It’s not so much food for the soul (the Eucharist is that) as it is a sort of vitamin pill for the soul. If it turns out to be a fake, it turns out to be a fake. Other fakes have happened. But nothing in the core of the Faith changes.
I have an issue with Mark. He tends to conflate those who think it might be a natural image with those who think it is a fake. He also over simplifies. Plenty of Christians, too, think it is natural or think it is fake. But then he qualifies his ascertains:
Still, I have a high degree of confidence this will not turn out to be a fake, not because I believe it to be the burial cloth of Jesus by faith, but for much the same reason I have a high degree of confidence that Lee Harvey Oswald shot President Kennedy: because it’s the most sensible synthesis of the available physical evidence. I have nothing riding on the authenticity of the Shroud. I just think it’s the best explanation of all the data.