Here's a fact that cuts against your case: belief in God is highest in the poorest, most suffering-racked countries and lowest in wealthy, safe ones. If suffering made God unlikely, you'd expect the opposite. Now, your unfalsifiability worry is fair, I'll grant it. But notice both sides lean on hidden reasons: you need "this suffering is pointless," I need "maybe it isn't." That's an impasse, not evidence of absence. So suffering stays a puzzle, and a puzzle isn't a verdict.