Noah's was the tenth generation from Adam. By the time of the flood in 2348 B.C. (based upon Ussher's chronology), all nine of his ancestors were gone. Eight had died and Enoch "was not for God took him" (Gen. 5:24). In Genesis 6:7-8, we are told that mankind was so evil that God decided to "start over." Out of all the wicked men on Earth, He chose to begin with Noah, who most mistakenly think of as a righteous man. That is understandable because he is called "just" (Gen. 6:9); "righteous" (Gen. 7:1; Ezek. 14:14, 20); and "a preacher of righteousness" (2 Pet. 2:5). Because "there is none righteous, no not one" (Rom. 3:10), God's Word teaches that Noah acquired the status of being righteous the same way Abraham did. Abraham believed God and it was counted unto him for righteousness (Rom. 4:3, 9, 13; Gal. 3:6; Jam. 2:23). In Ephesians 2:8, we see that even the faith to believe in God is a gift from God. Notice Noah is called "just" after he had "found grace in the eyes of the Lord" (cp. Gen. 6:8 and 6:9). "Grace" is unmerited favor. Noah's righteousness was received just as you and I received it when we placed our trust in Christ (Heb. 11:7).
When we realize that Noah was unworthy to escape the judgment of God upon the Earth, it makes it easier to understand why his experience is a good picture of the Rapture of the Church. First of all, none of us deserves to be a born again Christian, let alone be raptured. All believers from all dispensations have been given the faith that results in them being considered righteous. Jesus used Noah's example to explain how it will be when the Tribulation occurs (Matt. 24:37-39). Noah and his family were lifted up above the judgment taking place below. Sinners were and are saved from God's judgment by grace: Noah in the ark and Christians in the Rapture.
Noah is a good picture or type for the Church in another way. Christians are not perfect. We are far from it. Noah, following being saved from the flood, planted a vineyard, got drunk, had a run-in with his son, and cursed his grandson (Gen. 9:20-27). Like him, we will not be what we should be until "we be (sic) like Him" (1 Jn. 3:2)! Why Noah cursed his grandson, Canaan, I cannot tell you. But I do have a theory about Ham's transgression. It appears that Ham sinned because he saw his father naked. That always puzzled me because I do not see a problem with family members of the same gender seeing each other naked. Perhaps their culture was different, I don't know, but I found a passage of Scripture that helped me make some sense of it. In Leviticus 18:6-19, there is a long list of people who are not to be seen naked. In each case where a male is mentioned, he is married and the prohibition is against looking upon the male's wife. When a person sees the nakedness of the wife, it is deemed disrespect for the husband, for married couples are considered to be one. The nakedness Ham may have seen could have been that of his mother. However, it was Noah who was drunk, so who knows.
The ark and the Rapture: sinners being lifted up above God's wrath below. "For God hath not appointed us to wrath, but to obtain salvation by our Lord Jesus Christ" (1 Th. 5:9). So be comforted (1 Th. 4:18; 5:11). Hallelujah!