The KEY word is "unauthorized" and the results cannot be published although they are talked about among Shroud investigators. The Church did not authorize the C14 test on one of the threads taken in 1978 but it was done. The results strongly suggest that the main body is first century. With modern C14 small sample methodology and accuracy, a few 1 cm threads would be sufficient for numerous tests.
The hard part is warping the loom. Warping requires planning, measuring and mathematics. When you weave wool, you must starch the thread because wool is flexible and stretches and causes all kind of limpy, saggy, problems. But you starch linen because it won't stretch, is inflexible by its nature, and will break.
I keep saying this because a twelve-yard piece of linen fabric that survives two millenniums is completely miraculous without any graphic depictions. Understand that such a textile, without the graphic, is already miraculous.