I can't prove it more than anecdotally, but I believe evolution has purpose and direction. It appears obvious, yet absolutely unconfirmable, that matter is groping towards complexity. While the laws of nature—and time itself—require objects and life forms attain durability and sustainability for survival, it seems to me more a means to an end than an end in itself.
Theology goes a long way towards imbuing substance and processes with meaning—describing life as "matter reaching towards divinity," or as the process through which divinity calls matter back up into itself—but theologians repeatedly make the mistake of ascribing this sense of purpose to history rather than the future. This is only natural, since the narrative structures we use to understand our world tend to have beginnings, middles, and ends. In order to experience the pay-off at the end of the story, we need to see it as somehow built-in to the original intention of events.
It's also hard for people to contend with the great probability that we are simply over-advanced fungi and bacteria, hurling through a galaxy in cold and meaningless space. Our existence may be unintentional, meaningless and purposeless; but that doesn't preclude meaning or purpose from emerging as a result of our interaction and collaboration. Meaning may not be a precondition for humanity, but rather a byproduct of it.
That's why it's so important to recognize that evolution, at its best, is a team sport. As Darwin's later, lesser-known, but more important works contended, survival of the fittest is not a law applied to individuals, but to groups. Just as it is now postulated that mosquitoes cause their victims to itch and sweat nervously so that other mosquitoes can more easily find the target, most great leaps forward in human evolution—from the formation of clans to the building of cities—are feats of collaborative effort. Better rates of survival are as much a happy side effect of good collaboration as their purpose.
If we could stop relating to meaning and purpose as artifacts of some divine creative act, and see them instead as the yield of our own creative future, they become goals, intentions, and processes very much in reach—rather than the shadows of childlike, superstitious mythology
The proof is impossible, since it is an unfolding one. Like reaching a horizon, arrival merely necessitates more travel.