The Shroud is hard (well, okay, “soft”) evidence. The growth of the Church, the conversion of Paul, the Gospels, the continuity with the Old Testament prophecies, the destruction of Jerusalem, the martyrdoms of the disciples and Apostles are all evidences in the sense of these all need to be explained by whatever brought them about. There is no reason not to side with the best explanation as far as the entirety of events is concerned.
As for Kierkegaard, as much as I think he was a master of identifying and explicating what it means to be Christian by way of an intensely personal depiction of it, he wasn’t Catholic in the sense of seeing what that first person account means relative to belonging to the community of saints as a member of the Body of Christ.
Kierkegaard would, himself, admit that his role was to be a keen observer of what it means to be a Christian, not that he, himself, necessarily was one, perfectly.