God only knows
Looking at the current one it is clear that, whatever it is, it is not an obvious fake. Moreover, the muscle definition of the body is simply far beyond any medieval art. It is either a genuine miracle, but showing serious errors on God's part, or an article created by some unrivalled Renaissance artist using a camera obscura (something da Vinci was interested in) and recently available silver sulphate (he was also interested in chemistry). If that technique is accepted, a medieval origin is also impossible.
I do not exclude the possibility that the universe has some sort of self-aware creator, but I do exclude as unreasonable that He would have spent time creating the shroud, in France in the 14th century, in a way we can now duplicate, and got it wrong in this way.
For God to impersonate da Vinci is not quite as great an achievement as for da Vinci to impersonate God.