The foundation of the Buddhist religion is that life is suffering. But I don't think even they believe God "invented" suffering.

I don't know how to explain lives that are entirely pain and deprivation, such as some of our fellow autistics that were warehoused in abusive institutions. My understanding is that we experience everything through cycles of rebirth until we learn balance.

The "suffering" that most of us complain about is a form of entitlement. It is what helps us to grow and define priorities. Maybe "God wants" us to be strong and wise.

But these discussion points are what religion is for, for they cannot really be answered scientifically, which always requires measurements.