2 Kings 19:35 states 1 angel killed 185,000 Assyrian soldiers while they were sleeping. A global flood seems rather silly. There is no evidence of a global flood. It seems the global flood in Genesis was plagiarized from the Sumerian epic of Gilgamesh.
With that being stated, the Epicurean ideology or philosophy of the "Problem with Evil" isn't proof of there being no god or that if there is a god this god is uncaring.
Pain and suffering are not the same. Pain is inevitable. Suffering is a choice. Suffering is how we respond to pain. Animals do not suffer. Some animals and organisms are not even capable of feeling pain. Pain is a safety mechanism to protect us from harm.
Consider that suffering and pain are often confused, but in fact are not identical. Pain produces suffering, but suffering can be produced by things other than pain, generally speaking by negative emotional states. That pain and suffering are not identical is also shown by the fact that people may experience pain and not suffer from it.
As far as where the human concept of empathy comes from - evolution. Primates have developed a sense of looking at something else in pain and the brain responding by basically saying "How would I feel if I were having that experience?" From this evolutionary advancement humans developed empathy which in turn gave birth to what we call morality. It is an advanced survival mechanism. Everything our body does, including brain functions, is a survival mechanism.
Philosophically, good cannot exist without bad as light without dark or pain without pleasure. The Hindu belief system describes all life as god, playing a part or a role in a drama that exists over an aeon. Like any drama, there is a protagonist and an antagonist. As long as good is winning and bad is losing we are content. However, we have gone astray with the idea that good must win and bad must lose. This would end the drama/play and the story would be over. Stories ending often generate anxiety. Anxiety is a form of suffering.