Although not enough information is provided, still we can do some analysis on it.
Case 1: "the anthropological evidence of universality"
This sentence would be okay as the postmodification "of universality" makes "anthropological evidence" definite. I know which anthropological evidence you are referring. So it would be okay to do that.
Case 2: "the anthropological evidence of the universality"
It may or may not be okay. Obviously, the universality is not some general knowledge that everyone is supposed to know. So you can't use a definite directly. You must mention it before you can use a definite article. It is called anaphoric reference.