Why would it be? Negatives cannot be “proven”. The atheists simply say that there is no visible positive side effect of pain and suffering. Their argument is the “duck principle”. And everyone uses the duck principle, both believers and infidels.
And “what” greater good are you talking about? It is your job to take each and every “seemingly” evil event and show that it was actually a blessing in disguise. Take the Holocaust and bring up arguments that preventing the Holocaust would have brought forth an even worse state of affairs.
That is the point. You cannot establish God’s existence or God’s “nature”. All you can do is observe the physical existence, here and now, and you can try to extrapolate from your observation. And it definitely does NOT point to a loving, caring God.