According to theistic evolutionists, at what point did humans evolve enough to be considered special to God? Disclaimer - Even though my personal views are well-established, I'd like to point out that I am not out to make a point with this question, and I am absolutely not out to establish whether any specific perspective is true.  I am simply curious about this.  I know the atheistic views, I know the day-age theory, the gap theory, etc, but I've never heard an answer to this, good or bad.  I'd like to know what the answer is from those who genuinely hold this view.

Theistic Evolution defined from Wikipedia:


  Theistic evolution or evolutionary creation is a concept that asserts
  that classical religious teachings about God are compatible with the
  modern scientific understanding about biological evolution. In short,
  theistic evolutionists believe that there is a God, that God is the
  creator of the material universe and (by consequence) all life within,
  and that biological evolution is simply a natural process within that
  creation. Evolution, according to this view, is simply a tool that God
  employed to develop human life. According to the American Scientific
  Affiliation:


In general, most Christian teachings assert that the relationship between God and Man is unique, and different than the relationship between God and other animals.  

Assuming that theistic evolution is a valid point of view (and I'm not arguing that it's not), are there any established teachings from any denomination or proponents that explain at what point we evolved enough to have a unique relationship with God? 

Barring that, what characteristics had to be present in order to have said relationship?  The ability to speak?  Cognitive reasoning?

The Wikipeda article lists several denominations that hold a theistic evolutionary view.  I'd like answers/reasoning from any of those perspectives, or from any established organization that holds/defends this view.
My lay, minimally-researched Catholic understanding may not necessarily qualify, since Catholicism doesn't require a belief in evolution. But ... well, here I go:

In my understanding, it would be the first creature capable of bearing God's image. That is, it would be the first creature capable of love, but with freedom of will, and capable of contemplating the divine mysteries.


  The human person participates in the light and power of the divine
  Spirit. By his reason, he is capable of understanding the order of
  things established by the Creator. By free will, he is capable of
  directing himself toward his true good. He finds his perfection “in
  seeking and loving what is true and good.” (Catechism of the Catholic
  Church)


The whole chapter on The Dignity of the Human Person explains in great detail the aspects of being human make us "special" or "in his likeness." But, the summation, I think, is the capacity for Godly things.

And, perhaps more of a side note, another "qualification" for human "God likeness" would be a creature capable of dominating all other earthly creatures.


  Then God said: Let us make human beings in our image, after our
  likeness. Let them have dominion over the fish of the sea, the birds
  of the air, the tame animals, all the wild animals, and all the
  creatures that crawl on the earth. (Genesis
  1:26)


In any case, if you're after a particular point in time or creature to which we could say, here's the baby that broke the barrier, I'm not sure that's a wholly religious discussion. If we did venture such a guess, it would be whenever the anthropologists told us it was! But, I think the general criteria apply to both the creationist and evolutionist-leaning perspectives.