The short answer is: "men's" is correct. Let's look at a few different examples to see why. First, let's look at a word for which you add an "-s" to make it plural.

To show possession of these particular plural words, the correct way would be to treat them as singular: Men's wear. Children's wear . Source: http://crofsblogs.typepad.com/english/2007/07/mens-or-mens.html. @published is incorrect, but the confusion is understandable.

The desire to avoid dilemmas about plural possessive vs. plural attributive noun, or possessive plural vs. singular possessive, for words where these are pronounced identically. (E.g. how do we know whether to write "a ladies' man" or "a ladies man", "a dog owner's guide" or "a dog owners' guide"?)

Man is being used as a singular collective term describing all of humanity. I believe that the point is that "Gods" and "Kings" would be separate entities (or special distinctions) that would be distinguished within mankind or distinct from mankind.

"the history of man" https://www.merriam-webster.com/dictionary/man. This is fairly common usage in my experience. Saying "The man" has an entirely different connotation that relates to authority figures, whereas "a man" is commonly used to indicate an individual person.