So we know that when God made the earth and the Garden of Eden it was perfect (Gen 1:31). Then God handed it over to Adam, to have denomination over the whole earth. The Earth still belongs to God mind you, but he gave man charge over it:
"Then God said, “Let Us make man in Our image, according to Our likeness; let them have dominion over the fish of the sea, over the birds of the air, and over the cattle, over all the earth and over every creeping thing that creeps on the earth.”" (Gen 1:26)
"You have made him to have dominion over the works of Your hands; You have put all things under his feet" (Psa 8:6)
In essence God gave Adam a title deed to the earth. Pastor Chuck Smith says, "Under Jewish law whenever you sold property in the deed there was always a redemptive clause. You always had the right to buy the property back within a specified period of time providing you could fulfill the terms and the requirements that were written in the deed.
So wherever there was the sale of property, there was always two deeds that were drawn up. One deed was sealed and it was put away in a safe deposit. The other remained open and was kept by the person who sold the property. And in the time of redemption you would bring both deeds, the one that was open and the one that was sealed. And by the open deed you would prove that you were the one that had the right to redeem it. And in the redeeming of it, you would break the seals of the closed deed and you would fulfill the requirements therein, and thus, the property would revert to you."
When Adam sinned he in essence turned the title deed of earth over to Satan. Since that point Satan has been the God of this world (2 Cr 4:4). Likewise John says the whole world is under the control of the evil one (1Jo 5:19). Satan tempted Jesus by showing Him all the kingdoms of the world and said all the authority (of these kingdoms) would be given to Him if He would worship Satan. This claim of ownership was never contested by Jesus and Satan could not tempt Jesus with something he did not have (Luke 4:5-7). Matthew 12:26 acknowledges that Satan has a kingdom. The Book of Daniel (Dan 10:20) describes two spiritual principalities, the prince of Persia (Persia was the dominate power of that day) and the prince of Greece (Alexander the Great became the next power), indicating Satan does have influence over the kingdoms over the earth. In Ezekiel 28 Satan is described as the King of Tyre who was the real power behind the power of Tyre. Satan's man The Anti-Christ will have authority over every tribe, nation, tongue (Rev 13:7). Revelation 13:2 makes it clear this authority comes from Satan not from God, "The dragon (Satan) gave him his power, his throne, and great authority." As such Satan retains some of his old authority, he is allowed to present himself before God (Job 1:6, 2:1), and when Micheal the archangel disputes Satan over the body of Moses he doesn't dare to condemn him (Jud 1:9).
When Jesus came and died on the cross, He redeemed the earth back but hasn't taken possession of it yet. Some believe the first seal opened in Revelation is the title deed to the earth (Rev 5), and the point at which God fully takes it back. After the seven years of tribulation and the removal of Satan and those who have taken his mark, there is a partial restoration that takes place. Life span's are restored to pre-flood conditions, everyone will eat under there own vine meaning no one will go hungry, and animals will no longer eat one another or harm us. After those 1000 years death, the final enemy, is destroyed and everything is made new and perfect once again.
In conclusion, there is evil and suffering in the world because Adam opened the door to it when he gave the title deed to Satan. That means even God is not legally bound to intervene until the title deed is taken back. Yes God can do anything, but He does have self-imposed limitations. If God violated his word then He wouldn't be a just God. But He has a plan to bring everything back into perfection, we are merely living in the intermediary period until then.