As you noted, the Great Flood story is detailed to even the day. The wording shows us in 3 different ways (making it indisputable) that only Noah, his wife, his 3 sons, and his sons’ wives got into the ark, and only they got out later. That point, some math, and the detail below, lead to one conclusion. A man can’t possibly become a father when his child is born; his fatherhood can only begin when the child is conceived. Otherwise, our math will be wrong, and below is just one of 3 such cases. In this case we have about 2 years to reconcile (See Reconcile about 2 years below). For the other 2 cases there is only 1.
First though, when we look at the flood’s detail in dates, spans of time, ages, etc. from an accounting perspective, we’ll see 3 different ways (making this also indisputable) that the flood’s span of time or how long Noah stayed on the ark, from when the floodgates were opened to when the land was dry again, was just beyond one year. Per Genesis 8:13-14 less Genesis 7:11, the flood lasted exactly 1 year and 10 days.
Gen 7:11 In the 600th year of Noah's life, in the 2nd month, the 17th day of the month, the same day were all the fountains of the great deep broken up, and the windows of heaven were opened.
Gen 8:13-14 And it came to pass in the 601st first year, in the 1st month, the 1st day of the month, the waters were dried up from off the earth: and Noah removed the covering of the ark, and looked, and, behold, the face of the ground was dry. And in the 2nd month, on the 7th and 20th day of the month, was the earth dried. (KJV)
(601 year’s and 2nd month’s 27th day less: 600 year’s and 2nd month’s 17th day = 1 year, 10 days).
While we can’t prove that to the day again, we can confirm in two other ways the flood definitely lasted more than 1 year.
Estimate #1 is 373 days:
This we could reach by focusing on water movement, mostly the two sets of 150 days.
-150 days from Gen 7:24-8:2 "The waters maintained their crest over the earth for 150 days, and then God...made a wind sweep over the earth, and the waters began to subside. The fountains of the abyss and the floodgates of the sky were closed, and the downpour from the sky was held back."
-150 then from Gen 8:3-4 "Gradually the waters receded from the earth. At the end of 150 days, the water had so diminished that, in the 7th month, on the 17th day of the month, the ark came to rest on the mountains of Ararat."
-73 additional days we would need to add. That is how much longer it took for the land to dry, the time from Gen 8:4 to Gen 8:5.
Gen 8:5 "The waters continued to diminish until the 10th month"…
less: Gen 8:4 "...in the 7th month, on the 17th day of the month..."
With Gen 8:5, about 270 days had gone by (9 months passed * 30 days/month = 270 days)
With Gen 8:4, about 197 days had gone by ("...in the 7th month, on the 17th day of the month..." says 6 months and 17 days had passed (6 months * 30 days per month = 180 days, + 17 days = 197 days had gone by)
The net of 270 - 197 is 73 days.
This estimate's total is 373 days (i.e. the 150 days + the 150 days + the 73 days = 373)
Estimate #2, which is from a 3rd way of measuring, is 382 days:
This we'd reach by focusing on the diminishing waters, but passing all verses until Gen 8:5.
-271 days from Gen 8:5 "The waters continued to diminish until the 10th month, and on 1st day of the 10th month the tops of the mountains appeared." By the 10th month, 9 months had passed. [(9 months * 30 days per month = 270) + 1 day = 271 days).
-111 days is about how many we'd need to add here. Counting this way we'd have to add the 40 days before Noah opened the hatch, the 7 days before he sent the dove that returned with a leaf, the 7 days later he again sent the dove that never returned and 57 days in Noah's "601st year of Noah's life" that the water was drying.
Gen 8:14 "In the 2nd month, on the 27th day…the earth was dry."
(2nd month's 27th day means about 57 days have passed. (1 month * 30 days/month + 27 days = 57).
The net of the 40 + 7 + 7 + 57 is 111.
This estimate # 2's total is 382 days (the 270 + the 111).
Even though we're estimating with math using 30 days/month, etc., each of the 2 estimates is definitely more than 1 year.
Next, since the span of the flood was just beyond a year, everyone’s “years old” went up by at least 1. While a child could have been born in the ark, he would have had to die in it too; that is because no child left the ark.
Reconcile about 2 years: When we combine the next 3 verses from 3 different chapters, we seem to have about 2 years to explain.
Gen 5:32: And Noah was 500 hundred years old: and Noah begat Shem, Ham, and Japheth.
Gen 7:11 In the 600th year of Noah's life, in the 2nd month, the 17th day of the month, the same day were all the fountains of the great deep broken up, and the windows of heaven were opened.
Gen 11:10 These are the generations of Shem: Shem was 100 years old, and begat Arpachshad, 2 years after the flood. (KJV)
[If Noah was 500 years old when Shem was born and 600 at the start of the flood, then Shem would have been 100 at the start of the flood. The last verse above says he was 100 "2 years after the flood." Thus we have to explain about 2 years.
Note: At the same time, we'd be incorrect in saying "The words '2 years after the Flood' are just a mistake". If we deleted those 5 words, you can see we'd have Noah being 600 years old when the floodgates were opened; if Shem was 500 years younger, he'd have been 100 years old then (600 - 500 = 100). Since Shem begat Arpachshad when he was 100, the child would have had to be born on the ark. However, no child left the ark].
Let's temporarily assume that fatherhood begins at conception, working only with those 3 verses for now and doing the math.
Gen 5:32: And Noah was 500 hundred years old: and Noah begat Shem, Ham, and Japheth. (KJV)
(Noah was 500 years old when Shem was conceived, but Shem wouldn't be born for about 9 more months. By the time Shem was born, Noah would probably have been 501 years old. Noah would then have been 501 years older than Shem).
Gen 7:11 In the 600th year of Noah's life, in the 2nd month, the 17th day of the month, the same day were all the fountains of the great deep broken up, and the windows of heaven were opened. (KJV)
(In the 600th year of Noah's life, his age was only 599. Again, his life began at his conception too.)
(Based on the two verses just above, Shem would have been only 98 years old when the floodgates were opened; that is Noah's age of 599 when the flood began less: the 501 years Noah was older than Shem).
Gen 11:10 These are the generations of Shem: Shem was 100 years old, and begat Arphaxad 2 years after the flood. (KJV)
(Since Shem was 98 years old when the flood began, 2 years later he would indeed have been 100 years old).
Conclusion to date: Fatherhood can only begin at conception, or the math is incorrect here and in 2 more cases. One other case is with Was or wasn’t Shem’s son Arphaxad born on the ark?, which holds different math problems using different sets of factors, excluding "2 years after the flood" for example. With that case there is only about 1 year that otherwise can't be explained. If fatherhood begins at conception, so do motherhood and childhood/life. Furthermore, that helps explain Joseph dies at about 110, with Joseph and his 110's shown twice in the final 5 verses of Genesis. In that case the author would have been writing about Joseph's life, for which counting began at conception, having 110 full years in it. Subsequently, in the final verse of Genesis and only 4 verses later, the author would have been writing about Joseph's age, for which counting began at birth yet the total years could be the same. (Otherwise, he'd be repeating someone's age at death, and Joseph would be the only one in Genesis for whom that would have been done).