“knew.” The word “know” is the common idiomatic word used for sexual intercourse. See commentary on Genesis 4:1.
“Cain knew his wife.” According to Genesis, Adam and Eve were the first two humans created, and Cain was the first son, so the question often arises, “Where did Cain’s wife come from?” The answer is that Adam and Eve had many children, and in those early years, and actually for many years after that, people married their siblings, their brothers and sisters, or married close relatives. The same thing happened after Noah’s Flood, and inter-family marriage still occurs today in some isolated family clans.
Genesis 5:4 says that Adam “became the father of sons and daughters,” and since those sons and daughters were the only people on earth in those early days, they married each other. The early chapters of Genesis spend a lot of time on genealogies and who gave birth to whom, and that in part explains where the people groups that populated the earth before the Flood, which we know little about, came from. The same emphasis on who gave birth to whom occurs again after the Flood when only Noah’s family was left on earth (Gen. 10:1-32; 11:10-30). Even Abraham, who lived more than 300 years after the Flood, married his half-sister. It was not until the Law of Moses was given to the Jews that God stated that people should not marry their close relatives, and the reason for that law was because people were in fact marrying their close relatives (Lev. 18:6; 20:17).
It is also important to note that when Genesis 4:17 says that Cain had a wife, there is no mention of the amount of time that had passed between Cain killing Abel and living in the land of Nod, and his taking a wife. In the days before the Flood people lived for hundreds of years, and so many years could have passed before Cain married. In fact, women have always married early in the biblical world, and given that fact, if Cain was 100 before he married, he could have married a woman that was five or more generations removed from Adam. That would have not been necessary, of course, Cain could have married a daughter of Adam and Eve that was closer to his age—the Bible just does not say.
A principle of correct Bible Interpretation is that if something was commonly done, or if logic and wisdom lead to a specific conclusion, then that conclusion is usually valid. For example, there are generally no references in the Bible to anyone going to the bathroom, but that did not mean they didn’t, it just means that it was so logical and necessary that there was no need to specifically mention it, and that same principle applies to a myriad of ordinary customs that were not written about.
Genesis is clear that Adam and Eve were the first two humans and they had sons and daughters who then married. In those early generations they married their relatives for the simple reason that there was no one else to marry. Over 2,000 years after God created Adam and Eve, He commanded in the Mosaic Law not to marry a close relative. There is no need to speculate and invent all manner of unbiblical ideas about other races on earth at the time of Adam and Eve, which contradicts the clear and simple Genesis account. Cain married his sister or a close relative, as did everyone else in those early years after creation. This is so logical that it is not specifically mentioned, just as it is not mentioned for the grandchildren of Noah.