Noah took a few years to complete constructing the ARK.
He was a prophet of GOD.
At the meantime, he had preached to his fellow people to repent and warned them about the flood. But they simply ignored his advice.
God had to punish the wicked generation accordingly, by his justice and sovereignty.
The babies offcourse hadn't sinned yet (but will sin when they grow up), God had the power to kill the adults and spare the babies, but the problem is, who will take care of the babies after the parents died?
To analyse this problem thoroughly, you must agree with the basic knowledge of bible about man's having physical body and soul, there is life after death.
If you disagree, then nothing can we discuss further!
A christian analyses problem of bible from the point of view of Secular as well as Spiritual world.
From the whole context of bible, man's existance does not cease after physical death.
Therefore, the fate of the babies who got killed in the flood did not end when there were drown.
God is just, he will not count those who are not guilty to be guilty, he will deal with their souls justly in another world.