The basis is simply that an omnipotent, omniscient being could have created the world in such a way where there is less suffering.
For instance, imagine a world without ebola.
...wasn't too hard to imagine, was it? God could do that. Why didn't he? Why did god create it in the first place?
Well then, this all boils down to one basic question - does God, assuming (from your point of view) that He exists, have free will?
There is no quick and easy, fast food answer to a question such as this. Only by beginning to see and understand the seamless garment of Truth that unites all things can we begin to gain insight into this topic.
So I suppose I will do my best to not "dodge" the question, but will offer a detailed reply. From there, you can decide if there is enough "evidence" (since that seems to be the key -SUBJECTIVE- term upon which many folks on these forums are so insistent ) to satisfy your inquiry. (Of course, no matter how much worthy evidence is submitted, "a man convinced against his will"...etc.)
Before time, before creation, all that existed was the Unspeakable Entity, the Eternal One. In the One existed and exists all things in the form of thought, seeds. Keeping in mind that man is made in the image of God, notice this observation: the seeds of an earthly man are a type and symbol of his thoughts, and vice versa. Thousands of thoughts on a given day are involuntarily generated within the mind of a man, just as thousands of seeds are involuntarily generated within the loins of a man throughout a given day. But only a small portion of those thoughts, throughout a day and a lifetime, are brought to fruition in the form of word or deed. Likewise, only a small portion, if any, of a man's seeds are brought to fruition throughout a lifetime, in the from of offspring.
Now that we see the parallel between thought and seed, we can continue our investigation into these trivial little matters and queries such as, oh, why and how we exist, why evil and suffering take place, if man has free will, and if God has free will.
In order for the One to bring Its thoughts, Its seeds, to fruition, it needed to no longer remain as one, but two become two, so that Its "seeds could be planted." Seeing as how the fullness of all things good consist in the One and of the One, in order for the One to have become two, it necessitated a split into the existence of a contrast, of enmity, something other than Itself. And since the fullness of all good consists in the One, this split necessitated the introduction of that which contrasts good - evil.
In order for God to be recognized as, and defined as God, and to be recognized as perfect, it necessitated the existence of something imperfect - creation. At the moment of creation, the One "became" God by creating something inferior to Itself. The Superior Being gains his identity as such by the existence of inferior beings; beings that can recognize and behold and define Him as the Superior Being.
Even as the male would not have his identity as a male apart from the existence of a female, so too does God not have His identity as God apart from the existence of creation that is subject to Him. Male and female help to define each other, even as Creator and creation help to define each other.
On this issue, the wisdom of Buddha shines forth in these words:
Nothing ever exists entirely alone; everything is in relation to everything else.
All of recognizable existence spawns from this basic element of the split. As a natural overflow of this, this is why only male/female unions have the capability to bring forth further life; and not male/male or female/female unions. Because male is not male without the existence of female, and vice versa. There would be no creation, no existence, if the One had remained One. In order to bring foth recognizable existence, the Great Entity had to split into a contrasting, male/female dual existence.
This is seen in the Genesis account of Adam and Eve. Adam the male existed solely unto himself, and, after being put to sleep, a part of his own being was fashioned into Eve the female.
So what is the significance of Adam being put to sleep (other than the obviouis truth that it would be a painful experience to have one's side opened up, and a body part removed)? Remember, as humans, we are made in the image of God. As such, the things we do and experience are just a smaller representation of God's own makeup and personality. As humans, when we dream, there are times when we (in our dreams) do or say things that are out of character for ourselves. For the most part (aside from the anamoly of lucid dreaming), we do not have control of what takes place in our dreams, even our own actions within them. And sometimes this leads us to dreaming ourselevs doing things and witnessing things that we would never do in waking time. But our human sleep is only a "type" of a higher spiritual reality. Now follow along carefully.
Because God represents the male (Adam), and creation that came from him represents the female (Eve), and because the ultimate destiny is for God to again become one and live in harmony with His creation (even as a male and female come together as one), at this time, his "female companion," His "Eve," is being formed. Even as Eve was taken as a part of Adam and then formed into a female as he slept, so too is God's creation being formed while He "sleeps." And, even as when we sleep and dream we have no real control of our dreams, and think things out of character for ourselves, so too is God dreaming and thinking things outside of His true heavenly, and fully good nature, and so too is His creation "out of control." This gives God an "excuse," if you will, for the existence of suffering and evil and the rampant chaos of the world.
Because all things that happen are taking place in the very mind of God, the bad things that are taking place are due to the fact that he is "asleep" and "dreaming" while his female "companion" is being formed, and being made fit to unite with Him; all of creation being destined to one day return to its divine nature and unity with the One from which it came.