God lets people die at an early age because it is his will to allow them to die. Whatever occurs does so by God's permission. Ephesians 1:11 says that God "...works all things after the counsel of His will." This does not mean that God has caused people to die at early ages. But it is his will to allow people to die early, just as it is his will to allow people to sin.
God does not want people to sin, but he lets them do it. God does not want people to rebel against him, but he allows it. Why? Because it is his will to permit people to rebel against him. If he stopped everyone from rebelling, there would be no freedom of choice, no freedom of will. But because we are made in the image of God (Genesis 1:26), we have certain responsibilities and one of those reponsibilities is to face the consequences of our choices. We would not be able to face the consequences of our choices if God never let us do things that were contrary to what he wanted in his "perfect" will. So, God allows people to rebel against him, and it is his will to do so.
We can now better understand why God allows people to die at an early age. Sin entered the world through Adam (Romans 5:12). Sin spread to everyone, and the effects of sin are not only upon the soul but also upon the body, as well as the world. This is why we have sin, sickness, and natural disasters. One of the effects of sin is death, and the effect of sin on people takes different forms. With some it might be early death, with others it might be a deformed limb, or blindness, or mental instability, etc.
So, God lets people die at an early age because it is one of the effects of sin in the world.