Why does God allow innocent people to suffer?
Well, God is not here to blame. We should blame ourselves if necessary! Because, God does not forcibly send us here. We asked free will and God gave us free will. God knew that we will not be able to manage our free will properly, still due to our insistence God eventually approved so, because God loves us.
[The Quran 33:72] We have offered the responsibility (FREEDOM of choice) to the heavens and the earth, and the mountains, but they refused to bear it, and were afraid of it. But the human being accepted it; he was transgressing, ignorant.
The above verse clearly indicates that God even did not very happy for our foolishness. Therefore, we are suffering here on earth due to our own choice. God is not unduly punishing us. This statement could further be supported by other Quranic verses:
[The Quran 4:79] Anything good that happens to you is from GOD, and anything bad that happens to you is from you…
So, for the huge sufferings of many innocent people on earth, God is not responsible. We have decided to come to this difficult world for some time and either we can choose good or bad paths and face the consequences accordingly. God not only gives us free will but also conscience.
Most of the sufferings here are due to human corruption, dishonesty, selfishness, foolishness etc. Of course, this physical world is very difficult place but our lives are here very brief too. So luckily it is not a perpetual suffering; it has a guaranteed end! God loves us very much and that is why our life here is very short.