Existence of evil isn't proof that [the Christian] God doesn't exist, for a variety of reasons, some less obvious than others. Although it's still very unlikely that he does exist.
Which is generally irrelevant, because faith is entirely separate from objective facts. You don't need to consider the hypothetical existence of God to be a true fact in order to be a good Christian. To 'believe' in him means something else completely, but depending on your language it might not make linguistic sense (assuming it makes sense at all, but that's a separate discussion).
The same is, however, not true for Catholicism, Orthodox Christianity (stupid ass name), Mormonism, or some others. Mostly because they have nothing to do with Christianity, and are just... well, scams.
Catholicism, and most other Christian denominations, use Christianity in a similar fashion to the Nazis using swastikas.
The main idea of Christianity is that earthly life is essentially an entrance exam for the next, true life. You live your life as best you can, then you're judged afterwards, and if you pass - you go to heaven, which is supposedly a paradise free of evil.
So evil (or what we generally consider to be 'evil') being omnipresent does not prove anything in the context of Christianity. The crucial part is whether or not evil exists in the 'next life'. Conveniently, we'll never know until we reach it, so it'll probably never be possible to prove anything on this topic.
I'm not sure if it's still possible to track where it all started, but to me it seems quite likely that precisely this idea of 'true life' or 'soul' being disconnected from physical, observable, empirical reality is where all our troubles with capitalism started.
If this life is largely meaningless, and the real one starts after we die, then sooner or later some people will just do whatever they want. And if humans are the only 'intelligent' beings, or the only beings with souls (Christianity + later Enlightenment philosophy), then mass destruction of nature is morally sound.
Then add focusing on accumulation of capital, as well as industrial machinery, and you arrive where we are today, pretty much.