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I can't think of any group that doesn't make the connection between sex and reproduction but there are/were cultures that don't understand it in its entirety. In particular, there used to be many societies who believed in multiple paternity, where a baby can have multiple fathers if a woman has sex with multiple men. You can find this belief among several Amazon tribes as well as ancient Hawaii.
Edit:
I've been doing some reading and it appears that among one tribe in New Guinea people didn't make the connection between sex and reproduction at all, so families were matrilineal. The people proved this because a man's wife could have a child even when he's been travelling for two years. (Scientific explanation: adultery.) They also understand that reproduction works the same for all animal species and their pigs reproduce even though they castrate all the males. (Scientific explanation: domesticated female pigs mate with wild pigs.)
Upvote:4
From Robert Graves' The Greek Myths :
Once the relevance of coition to child-bearing had been admitted - an account of this tuning-point in religion appears in the Hittite myth of Appu (H.G. Guterbock: Kamarbi, 1946) - man's religious status gradually improved, and winds or rivers were no longer given credit for impregnating women.
So this view identifies a date of between 1600BCE and about 1200BCE.
Interestingly, Graves notes that this change in outlook coincides with the change from matrilineal societies to patrilineal societies.
In the Myth of Appu, poor old Appu is busy sacrificing sheep to the gods when, according to the wikipedia article -
The sun-god appears and advises him to get drunk and then have sex with his wife.