What if God left a real intriguing clue that the man who died, whose head was covered by the shroud, was truly divine? Say, for example, that the human DNA residue was a “perfect” or otherwise humanly impossible sequence. Now THAT would be wild!
Then people would just worship the source of that DNA as an icon. Through history God seems to have strenuously avoided doing things just like that. There's a reason there are no contemporary portraits of Jesus.