Can the Singular “Man” Refer to Mankind in General?

I am working through the definitions of the vocabulary in my textbook, Basics of Biblical Greek, and got to wondering about ἄνθρωπος. I am trying to lay out the vocabulary in a way that doesn’t mash all the different meanings of a word into one long definition but recognizes the categories of meaning most words enjoy.

I was surprised when I went to BDAG. It has nine categories of meaning, but the main two are:

Definition 1. “a person of either sex, w. focus on participation in the human race, a human being.” Glosses such as “person” (plural: “people”) and “human (being)” (plural: “humanity”) work well here.

Definition 3. “a male person, man.

To be sure, ἄνθρωπος in both the singular and the plural can refer to a human being(s) without reference to gender. That’s not the question. The question is, in the singular, can ἄνθρωπος refer to people in general as implied by the gloss “mankind”? What was surprising is that BDAG does not have a category for this meaning, and I can find no clear-cut example of this in the New Testament. The closest is John 2:25, but that does not prove the point.

Some of the references are to a single male who stands as an example to all people, but that still is not what I am looking for.

This is a really important issue, because the glosses we memorize tend to control our thinking about the basic meaning of a word and how we approach translation.

Help me out on this. Can anyone find a clear example of ἄνθρωπος in the singular referring to people in general and not to a single human being regardless of gender?