Why did God choose Moshe? The Torah says very little about him, other than that he was extremely humble. However, I heard from a tape by Rabbi Kardozo that his humility stemmed from his being in such close contact with God, hence he was not as humble before God spoke to him.
Is there a source for why God specifically chose him? Or perhaps he was simply destined from birth?
From here:
The Holy One tested Moshe by means of the flock, as our sages have explained: when Moshe was tending Yitro's flock out in the desert, a lamb ran off, and Moshe followed it, until it found shelter under a rock. There it found water and stopped to drink. When Moshe approached the lamb, he said: "I did not know that you ran away because you were thirsty. Now you must be tired." So he put the lamb on his shoulder and walked back with it. The Holy One then said: because you showed such compassion tending the flock of another person, as you live, you shall become the shepherd of Israel, the flock that is Mine. Thus it is written: "Now Moshe was tending the flock. . . " (Midrash Shmot Rabbah, 2:2; adapted from Braude translation.)
On the other hand, even from birth it was recognized the Moshe was special, see Rashi on Shemot 2:2:
that he was good: When he was born, the entire house was filled with light. [From Sotah 12a, Exod. Rabbah 1:20]
Nechama Leibowitz has an explanation that (IMHO) beautifully combines peshat and midrash. She notes that, leading up to Moshe's prophecy at the bush, there are three progressive stories recorded about him.
The first is the story of him seeing an Egyptian oppressing a Hebrew, in which he kills the Egyptian. This demonstrates how strongly he felt about saving the oppressed, but one might think that he only got involved because he was defending a member of his own people against the enemy. Next, however, we see him getting involved in a fight between two Hebrew men, showing that Moshe was a man who wanted to stop fights even within his people. Finally, we find that after he runs away, he defends the daughters if Yisro from the shepherds. Despite the fact that these women were perfect strangers, Moshe's sense of injustice was so strong that he was ready to assist anyone who needed help, no matter who they were.
The midrash (Shemos Rabbah 2:2) picks up on this trend, by developing it a step further: Moshe was tending to Yisro's sheep, and was willing to help even a single lamb get to the sustenance that it needed. The point that the midrash is bringing out relates to this portrayal of Moshe as a defender of the weak and righter of injustices, a man who deserves to lead a people.
I heard a drashaonce from Rav Elya Brudny regarding what Moshe did special that he was chosen to lead the nation. He said Moshe's ability to notice the fact that the bush was burning but was not consumed is what got him appointed. Anyone else would have seen a bush burning, glanced only momentarily, and assumed it was being consumed. Moshe was the type of person who would pay attention and see what was actually happening. This was a person worthy of leading and caring for the nation. Someone who would take note if something looked different than previously and deserved a closer inspection, instead of just relying on their own presuppositions.
From your closing paragraph it seems that you believe his being predestined is in contradistinction to having earned it. I would like to address that point. Moshe Rabbeinu wore many hats. Savior and redeemer. The one who accepted and presented the Torah. King and leader of the people for forty years in the desert. He was also a Kohein and Levy. Its possible he was predestined for any one or more of those while his appointment to any one or more was earned. We do find he lost the kehuna as Rashi brings in Shmos 4 14.
If I'm understanding your question correctly (i.e. destiny vs merit) then I don't necessarily see conflict as the two aren't mutually exclusive. The midrash (Tanchuma on Noach, 5 as well as others) asserts that Moshe was born circumcised; additionally, Rashi cites TB Sotah that the "house filled with light" signifying the special quality of the newborn. However, we also know that potential does not presume the fulfillment of one's destiny.
Indeed, Moshe carried within him tremendous capacity for action and was especially sensitive to matters of the spirit. But it was not until he demonstrated through his actions and intentions that he was worthy of the role of the "trustworthy shepherd" that he was chosen by God.
