The next-best evidence is what happened: apostles who had seen their master crucified became ignited with a zeal to make known the wonderful news that Jesus had risen from the dead.
Either the physical, bodily resurrection of Jesus Christ happened, or it didn't. If it didn't, then his disciples would have remained broken, dejected, disappointed at his death. If it did happen, then what happened would have happened... they would have done what they did, made known to the world the glorious truth that Jesus conquered the grave.
Placing faith in a cloth will ultimately lead to disappointment. Placing faith in the Risen Lord will never disappoint.
Christianity is laughed at as a religion of myth worshippers, hypocrites and worse. But still it goes on with the simple premise that we believe Jesus Christ died to somehow make us right with the Lord, he rose from the dead and that we were put on this earth by God in order to try to live our lives in harmony with his teachings...... and that God knowing what weak stuff we are made of has found it in his grace to forgive our sins if we only truly repent and give ourselves up to him.
I sure hope that God is a forgiving and patient master. I'm going to need all the help I can get.
Merry Christmas.... Jesus is born.