Are Children born crippled/diseased, uncared for, and dying prematurely proof that God does not exist?
If so,
1) What do children born healthy and well cared for prove?
2) What do babies aborted (many of whom might have led a normal healthy life, and some of whom might have contributed much to the society like many scientists, doctors, engineers ....) prove?
3) What do babies killed in wars (some of which are created for the sake of war) prove?
We have strength and intelligence to lessen/remove any such undesirable occurrences if we want to. (People who make to the Guinness Book of World Records show that seemingly impossible tasks are not so if we are determined to accomplish them)
Many people have had a fall in their bathrooms—yet effect varies from person to person—from no injury to serious injury (shows it depends on various factors or is determined by some laws). So is the case with drinking of alcohol—yet effect varies from person to person—from no health issues to serious health problems (shows it too depends on various factors or is determined by some laws). It is not proper to isolate one case from such varying effects and reach a conclusion. In big picture, everything happens by some laws working independently of God, and such laws may be perceptible or imperceptible, hence every effect should have some cause.
My experience is that God is confident of our abilities to solve any problem we experience, and will not listen to our prayers. See what happens when people use their intelligence and ingenuity. One zoo I visited has a separate enclosure where they bring babies removed from their parents after their birth. These babies who are deprived of the opportunity of seeing what their seniors are doing are learned new way of living as a family. Thus in this enclosure we find all animals—such as lions and lambs, cats and rats, snakes and frogs—living in peace.