Because of luck, i ended up discovering a version of the poem of Gilgamesh, and being a writer, interested in the history and mythologies that different humans have given to themselves with the pass of time, i couldn't restrain from trying to read it...
First of all... The introduction of the poem dates Gilgamesh as a king who reigned over uruk 2.700 years ago, so the first question is... 2.700 years ago or 2.700 years before christ? Because 2.700 years ago was the times of plato almost, not really that much ancient. And I'm not gonna get into "was it real?" Because I'm used to debates like this about el mio çid campeador or Roldan etc. Who the hell knows, i just wanna know what's a coherent estimation of the time in which he would have reigned over uruk.
Second of all... The poem, subtlety suggests in a way some kind of link between raw force of the individual's body and their ability to be king while not making much mention to intelligence or wisdom regarding Gilgamesh. I may habe skipped that part without being aware, I'm not perfect, but what I've read at least yet was a long list of how the guy was this kind of superman with "muscles of stone" and took away the sons of the fathers to make them pulp and took the daughters from their mothers in order to "own them" (We talking about no economic transaction here, i guess...). I wanna know if this is reflective of a concrete social mindset or just a literary trope.
And now, third of all and most interesting... Why... God why... Why a nun masturbating in the middle of the forest and fucking him during 7 days "in which he remained erect" (I'm quoting the book i swear) would give him the ability of reason, the ability to talk, and the ability to be civilized?
u/Bentresh has some good recommendations on translations and supplementary books, like Louise Prykes' book on Gilgamesh (which is available on Amazon, including kindle - their link's link to amazon doesn't work but it's there). The epic may be a little inscrutable without some guidance.
That user and those resources should be a good start. What I can help with right now is that Gilgamesh was a legendary king of Uruk circa 2700 BC, if he existed. Uruk is of paramount importance in the early history of urbanization and civilization in Mesopotamia (see: the Uruk period, about 4000-3100 BC). 2700 BC is in the early dynastic period, the beginning of dynastic kings ruling the city states of Mesopotamia, and only a few hundred years after the full-fledged development of writing in the region. Needless to say, specific details are scarce (but there's probably more than you'd expect!).
It's also important to note that while Sumerian and Akkadian are deciphered it's not as comfortable a translation process as say, ancient greek or Latin. I'd take a look at translations - you mentioned a nun, in fact Shamhat is a prostitute...but that's not really the best word either. It's complicated but nun doesn't seem right - she's a civilizing influence, bringing the knowledge of the urban world to Enkidu (not Gilgamesh, in case you missed that). There were nuns in that time, the naditu (though nun again isn't a perfect word they were women who lived cloistered lives and had a religious role), but I don't think that applies to Shamhat. Edit: there were naditu in the old Babylonian period, not necessarily in the early dynastic, I meant.
As far as the role of wisdom, the epic opens with that. To quote the book by Prykes (which I'm reading now, coincidentally!): "The prologue’s description of Gilgamesh recounts his achievements, and describes how he gained his exceptional wisdom."