Make no mistake, God does care! There is no heart as big as God's heart. There is no love like God's love; in fact, there is no love without God's love. And let it be said, God loved Noah.
Chapter 8 starts, "And God remembered Noah..." Of course, it says that he remembered the cows too. This is the God who superintends in the falling of a sparrow (Luke 12:6-7) and respects kindness to animals (Proverbs 12:10). It's just the nature of our God. He is patient. He is kind. He is sympathetic. He is troubled by suffering.
When anyone suffers, we can be certain that God must have some very high purpose in allowing that pain. God never bashes heads for the fun of it (Ezekiel 33:11). He is touched by the emotions that He sees in us.
So, in this case God expedited the departure of the water because of (it seems) the situation in the ark. Cabin fever I suppose? They had been on board for about half of a year at that point. It is noteworthy that even after God "felt sorry" for the folks in the boat, they still spent many more months on board before Noah "removed the covering" (after a total of one whole year on the ark).
Lesson: just because we are not immediately delivered from adversity, that doesn't mean that God doesn't "feel sorry for us" . . . it just means His timing is not ours. Remember, He does everything well. Trust that the various ingredients (God's wisdom, sovereignty, compassion, etc.) are all always perfectly balanced. God can't improve.
So, God sent the survivors off saying, "Breed abundantly in the earth, be fruitful, and multiply." Notice that God didn't JUST deliver Noah for Noah's own benefit. None of us exist for our own pleasure (neither does God exist for our pleasure); we exist for His purposes and His pleasure. While we enjoy God's goodness, let us always invest it in accordance with God's will. God saved Noah to use Him to refill the earth.
At this point, Noah understood his place. He built an altar to God and offered many animals on it as sacrifices to God's glory. Then, in receiving those offerings from Noah, God was moved to make a compassionate decision. He told Himself, "Even though the imagination of man's heart is evil from his youth... I will not smite everything any more... as I have done." He determined to keep things the way they were (and are) until the very end of man's cursed existence on this cursed planet. In other words, He purposed to be merciful DESPITE the certainty of future moral failures in humanity.
God is caring? Don't ever doubt it. He cares!