The weave used is the biggest clue.
Why is that, CodeToad? What makes you think that a three-over-one weave was beyond an expert weaver in 1st Century Judea? Do you think it is such a difficult thing to pick up three threads instead of one or two? There are surviving examples from that same period and area of woven cloth made of Byssus, the tendrils of a sea urchin, the absolutely finest cloth in the world. Why would a three-over-one twill somehow be beyond the skills of an expert weaver in the same area?