Adam wasn't alive in Gen 6.
Lamech, Noah's father was 56 when Adam died. Genesis 5 is not necessarily the account of every first born son. It is the account of the son born who would arrive at Noah as a descendant of Adam. I would put Methuselah as the generation that was pronounced as being:
"And it came to pass, when men began to multiply on the face of the earth, and daughters were born unto them,"
It was Methuselah who would have had daughters and even sons before Lamech was born. Methuselah was 187 when Lamech was born. Obviously not his firstborn. Perhaps not even the first born son. Lamech was the Father of Noah. Noah was born when Lamech was 182. Notice Genesis 5:28-29:
"And Lamech lived an hundred eighty and two years, and
begat a son: And he called his name Noah, saying, This same shall comfort us concerning our work and toil of our hands, because of the ground which the Lord hath cursed."
So Noah was not necessarily the firstborn, nor even the firstborn son. But Noah was a direct descendant of Adam. Methuselah lived for 969 years. Adam was still alive and still having children when Methuselah was born. But the next 900 years during Methuselah's life, the sons of God had offspring as well for hundreds of years. It was not the generation created on the 6th day, but their offspring started to procreate with Adam's offspring. But it was only Noah and his 3 sons born when Noah was 500 years old who were spared. Noah had no daughters on the ark, so no males came on board not from Adam's flesh. Noah's wife, nor the other 3 females had to be direct descendants of Adam and Eve. They could have been from those sons of God created on the 6th day. It was Adam's flesh that carried death and decay. The sons of God had permanent incorruptible physical bodies, that just became more corrupt with each generation mixed into Adam's dead corruptible flesh.
It was Adam who disobeyed God. It was just natural that Adam's flesh would corrupt the whole earth eventually. The sons of God could not remove Adam's dead flesh with their own genetic offspring.