Here is some background on the birth of Moses brought from the medrashim...
http://www.chabad.org/library/article_cdo/aid/111874/jewish/The-Birth-of-Moses.htmTHE LITTLE PROPHETESS
Life had become very difficult for the children of Israel in Egypt. Every day brought with it a new and more cruel decree from King Pharaoh, making life very miserable for the poor and, enslaved Hebrews. But there was at least one family which kept up its spirit and brought hope and courage to the others. That was the family of Amram, the son of Kehot great grandson of Jacob. He and his wife Jocheved, had two small children called Miriam, and Aaron.
One day Miriam went around in the house clapping her hands and saying, "I am going to have a little brother who will save our people from the hands of the Egyptians!"
And Miriam's words soon came true.
On the seventh day of Adar a baby boy was born to Amram and Jocheved, and immediately, the house became full of light. The clouds cleared and the sun shone more brightly than ever before. Amram came to his little daughter and kissed her, saying, "My darling daughter, I see now that you were right. Your new brother is not an ordinary baby. He will be the salvation of us all."
For three months the happy parents hid the newly-born baby from Pharaoh's officers who were going around from house to house, searching for Jewish babies, in order to throw them into the river, on orders from the king. At the end of three months, the officers began to search Amram's house very carefully, and Amram and Jocheved knew that they could not hide the little baby any longer. And so, Jocheved said, "I cannot protect my baby any longer, only G-d can. I will entrust my baby into His hands."
Saying this, Jocheved made a little basket of light weed, and covered it with pitch from without to make it watertight. "Let my baby not suffer from the smell of the pitch," she said, and that is why she did not pitch the basket from within. She then placed the baby into the water-tight basket, and took it down to the River Nile. She hid the basket among the papyrus reeds growing on the bank of the river.
II.
THE FATEFUL DAY
With tears in her eyes, she came back home. But little Miriam remained by the river's brink to see what would happen to her little brother.
At that very time, the Angels assembled before G-d and pleaded for the little baby. "Oh G-d," they said, "Thou hast promised that the day would come when the children of Israel would be delivered from Egypt and given Thy sacred Torah on the sixth day of Sivan. Today is the sixth of Sivan, wilt Thou let this child succumb to starvation and exposure in the waters of the Nile?"
Immediately, G-d ordered the sun to blaze away with might and main and cause all the Egyptian women and children to flock to the river to bathe and refresh themselves in the cool waters of the Nile.
Princess Bithiah, King Pharoah's daughter, called her maids and also went down to bathe in the river.
Suddenly, the princess noticed a little basket in the reeds by the river's brink. She sent one of her maids to fetch it, but her wicked maid said, "Why bother, princess, with a little basket where surely a Hebrew baby is hidden? Has not our mighty king ordered all the children to be thrown into the river without pity?"
Now the princess had lost the use of her arms through illness, and thought: "If only I could use my hands, I would fetch the little basket myself." No sooner did that kind thought flash through her mind than a wonderful thing happened to her. She suddenly felt that her hands were well and strong again. The princess went down among the reeds and picked up the little basket with her own hands.
When she opened the basket, she found there a little baby with a bright face that shone like the sun. The princess took pity on the baby and said, "Surely this is one of the unfortunate Hebrew babies. I will not be as cruel as my father; I will save him."
III.
IN HIS MOTHER'S ARMS
The princess ordered one of her Egyptian maids to feed the child. But as soon as the woman took the baby in her arms, he began to cry pitifully, and refused to be fed. The princess ordered another maid to feed the baby, but again with no success.
All this time, Miriam was standing only a little distance away, watching closely all that was happening to her little brother, but saying nothing. When she heard her little brother cry, she came forth and said to the princess: "Shall I call someone to feed the child?"
"Please do," said the princess, "and I will reward you amply."
Miriam hastened home to her mother, and told her all that had happened on the river's brink. "Hurry, mother," she said, "the princess is waiting, and the baby is hungry! "
Jocheved, rushed to the river and no sooner did she take the little baby in her arms, than it stopped crying and began to smile happily. The princess could not help smiling too, and she said to Jocheved, "I will pay you two shekels each day if you will nurse the baby for me."
"I shall be most happy to do so," Jocheved said.
"Good. I will entrust you with the baby for two years," the princess said, "but remember, that at the end of two years, you must bring the child to me at the palace safe and sound!"
"He will be the apple of my eye," Jocheved said, and carried the baby away to her home.
IV.
THE, SEVEN NAMES
Jocheved kept her promise, and at the end of two years, she brought the baby to the princess. Bithiah was delighted to see the baby. She had never seen such a beautiful and adorable child in all her life.
"What name do you call this child by?" Bithiah asked.
"We gave him six names," the mother said. "Jered, Chaver, Jekuthiel, Avigdor, Avi-Socho, and Avi-Zonoach!"
"I will give him a seventh name," Bithiah said. "I will call him Moshe (Moses), because I drew him out of the water."
And G-d said, "Because Bithiah was so kind and merciful, the child will be called by the name that she gave him."
From that day on, Moses remained in the palace and the princess loved him dearly, as though he were her own son. Everyone who came to the palace and saw Moses, admired the unusual beauty and good manners of the child. Even the cruel King Pharaoh and Queen Alpharaohnith loved him and played with him.
I am not suggesting he had 'face-to-face' prophecy before the incident of the burning bush... I am just suggesting that Moses was, from birth, destined to be the redeemer...