The years in the Genesis genealogies fit nicely into the chronology when we first notice that it doesn't say "When Adam was 130 years old...he became the father of Seth". That would require calculating speculations like 'was he 129 years and 7 months old, or maybe 130 years and 5 months old, or somewhere in between'?
It says "When Adam had lived 130 years, he became the father...".
So we start the timeline with Creation. Adam was created on day 6. We can start the clock now and count off 130 years. Next we're told "Seth lived 105 years, and became the father of Enosh", so we add 105 years and now we've counted off a total of 235 years.
This method can be followed until Noah, when we're told "Noah was 500 years old, and Noah became the father of Shem, Ham, and Japheth". NOW is when we see the phrase "years old" in reference to (apparently) the genealogy, but this number is irrelevant for our purposes because Shem is next in the lineage to Messiah, and he's not reckoned to the Timeline by when he was born.
The Flood started on the 17th day of the 2nd month, in the 600th year of Noah's life. The flood would remain on the earth the entire year, and as the water receded the mountain tops could be seen in the 10th month.
Then they came off the Ark in the 601st year of Noah's life, on the 27th day of the 2nd month. They were told to be fruitful and multiply, and fill the earth.
10 months later, after leaving the ark, was the beginning of the year that Shem's son Arphaxad was born. We know 4 things about this year:
- It was the 602nd year of Noah's life
- It was the year Arphaxad was born
- Shem was 100 years old
- It was 2 years after the Flood
"Shem was one hundred years old, and begot Arphaxad two years after the flood" (Gen. 11:10)
From here we continue as we did in the beginning: "Arphaxad lived 35 years, and begot Salah" etc. etc.