The fact that innocent babies and children suffer and die every day is proof that your god does not exist.
Not quite. It could be that this god is callous and indifferent. But yes, more likely non-existent.
The omnipotent and omnibenevolent god in whom JB believes cannot exist, given the contradictions we see in this world. This does not mean that it is impossible for a creator to exist, but it does mean that if there is one he is unconcerned with the plight of mankind. This would also mean he neither desires nor deserves our worship.