None of those are sufficient evidence of an all-powerful, all-knowing & all-loving god. You'll have to do better than that.
So, on this thread you have asked a few questions.
1/ If God is all-loving, then he would want to prevent these things.
2/ If God is all-powerful, then he would be capable of preventing these things.
and 3/ You are looking for proof of His existence.
For 1 and 2. Yes, God wants to prevent these things and He could, in one sense and can't in another. He is capable but cannot due to the fact that this is not the way He works.
All the troubles in the world stem from sin. Man causes his own problems. Greed, hate, selfishness, self love, lust for power and the belief that man is in control.
God made us with free will. Not even the purest human heart can live without causing pain and suffering to themselves or someone else.
God has a plan to stop all of this. It started with Christ on the cross. You accept this free gift of salvation. In the end, when time disappears and all the years of this age are gone, the men and women who chose the right path will live for eternity without pain, suffering or any issues of this evil driven world.
Until then, we are in this world but not of this world. Man, it's civilization and it's free will, will determine what events take place.
As for proof, it is by faith that we are saved. We cannot earn salvation. If you don't have a heart with an attitude of remorse you will never be able to see the proof. Proof comes after the attitude change.
All these people with the attitude that "these are dumb rules", or "that is wrong" "that's not the way it should be" "I want proof first"... they just don't get it. They are playing by their rules, the rules that man would have.
God wants the kind, humble, unconditional heart. Not the "ok, now I see the money, I'll take the job" sorta deal.
Once you can get to the point where you know you are lacking, you are a sinner, you need Christ, you can't do it alone and you have no right to demand anything different.... until then you will be blind to the truth, the proof, the glorious revelation of the truest love in the universe.
Once you see this, you will wonder how anyone could not.