God said unto Noah, The end of all flesh is come before me; for the earth is filled with violence through them; and, behold, I will destroy them with the earth. Make thee an ark of gopher wood; rooms shalt thou make in the ark, and shalt pitch it within and without with pitch.”
Genesis 6:13-14 KJV (https://www.bible.com/1/gen.6.13-14.kjv)
“But with thee will I establish my covenant; and thou shalt come into the ark, thou, and thy sons, and thy wife, and thy sons’ wives with thee.”
Genesis 6:18 KJV (https://www.bible.com/1/gen.6.18.kjv)
This means that Shem was 98 years old when the flood occurred making Noah 502 years old when Shem was born.
The earliest age a male was legally allowed to be married was the age of 14, so each son would probably be at least 14-20 years old when they were married, and if they were born 2-3 years apart, this would be a total time of about 18-26 years for them all to be married. This would make Noah at least 520-528 years old when he had all his sons married off and started to build the Ark.
Also after the Ark was built, it had to be loaded with food, supplies and animals. This was said to take 7 days.
“And the Lord said unto Noah, Come thou and all thy house into the ark; for thee have I seen righteous before me in this generation.
For yet seven days, and I will cause it to rain upon the earth forty days and forty nights; and every living substance that I have made will I destroy from off the face of the earth.”
Genesis 7:1, 4 KJV (https://www.bible.com/1/gen.7.1,4.kjv)
So, if Noah started building the Ark at the age of 520 and finished building it at the age of 600 minus 7 days, that means he would have taken less than 80 years [600-520] to build it. And notice that even if it took the sons longer than 20 years to be married, or if it took Noah more than 7 days to load the Ark with animals, supplies and food, it would still be less than 80 years to actually construct the Ark.