Lamech named his newborn son Noah, prophesying that he would bring comfort. This was about 1,000 years after the fall. Many had followed the ways of Cain and the lesser amount followed the ways of Adam. While Noah was born into a wicked world it would only get worse throughout his life.
Yet in the midst of this turmoil Noah was taught by his father Lamech and his grandfather Methuselah, both men knew both Adam and Enoch, who had both been in the presence of God. Noah was taught how to worship, develop faith in the Messiah and live righteously. He became a preacher of righteousness and a just man.
Moses tells us Noah walked with God 18 verses after he told us that Enoch walked with God. Obviously they had similar experiences. When Noah was 500 he had 3 sons, Japeth, Shem and Ham. These sons not only got to be taught by Methuselah and Lamech who would have taught them about Adam and Enoch but also their own father walked with God.
What is self-evident is that Noah would have had many sons and daughters during the 600 years from his birth and entering the ark. Not all followed in the ways of Noah. We are not told the details however life is life and the tests that come with following God are not easy. Especially when family do not follow in the path you have invited them to follow. All of the fathers from Adam to Jacob had this experience.
When the ark settled after the flood receded Noah offered sacrifice upon the altar. Moses only told us about Abel and Noah offering sacrifice, however it is clear to me that Adam would have been instructed by God and then shared that with his children. Both Abel and Noah did not just randomly do this. It was an important part of the worship of God from the beginning and practiced by the righteous from Adam to Jacob and to the time of Moses, who would have learned it from Jethro, a descendant of Abraham.
Noah lived for 350 years after the flood and witnessed wickedness enter the children of God again. Shem was blessed by Noah because he had shown by his life that he chose to serve God. Japeth was blessed also but Ham turned to the ways of Cain and as with Cain many of the posterity of Shem and Japeth gathered with the posterity of Ham and forgot God.