That's a matter of faith for you to wrestle with. . . but the Jesus of the Bible sat and talked, ate, walked, preached, and FACED the people of His time and nothing was written saying He hid His Face from them. If God allowed them to see His Face, why do you think He would not leave something behind to allow us to see it?
The carbon 14 test that actually put the tested age at approximately mid 14th Century were shown to be accurateon what they tested which was a re woven corner of the Shroud that intermixed original Shroud threads with about 50% SIXTEENTH CENTURY Cotten/Linen thread mixture that when tested return a spurious date of mixed old/newer carbon that averaged 1345 AD. The C14 test has been invalidated because of breaking of the sampling protocol.