Exodus 2

As Moses begins the record of his life, he provides very little detail of the first 80 years of his life.  What I find interesting is that upon the Pharaoh's daughter finding Moses, is the Josephus writes -

"Thermuthis was the king's daughter. She was now diverting herself by the banks of the river; and seeing a cradle borne along by the current, she sent some that could swim, and bid them bring the cradle to her. When those that were sent on this errand came to her with the cradle, and she saw the little child, she was greatly in love with it, on account of its largeness and beauty; for God had taken such great care in the formation of Moses, that he caused him to be thought worthy of bringing up, and providing for, by all those that had taken the most fatal resolutions, on account of the dread of his nativity, for the destruction of the rest of the Hebrew nation. Thermuthis bid them bring her a woman that might afford her breast to the child; yet would not the child admit of her breast, but turned away from it, and did the like to many other women. Now Miriam was by when this happened, not to appear to be there on purpose, but only as staying to see the child; and she said, “It is in vain that thou, O queen, callest for these women for the nourishing of the child, who are no way of kin to it; but still, if thou wilt order one of the Hebrew women to be brought, perhaps it may admit the breast of one of its own nation.” Now since she seemed to speak well, Thermuthis bid her procure such a one, and to bring one of those Hebrew women that gave suck. So when she had such authority given her, she came back and brought the mother, who was known to nobody there. And now the child gladly admitted the breast, and seemed to stick close to it; and so it was, that, at the queen's desire, the nursing of the child was entirely intrusted to the mother." (Antiquities of the Jews, Book 2, chapter 9, paragraph 5).

Of this same even, Moses writes of his mother that -

"...Pharaoh's daughter said unto her, Take this child away, and nurse it for me, and I will give thee thy wages. And the woman took the child, and nursed it.
10 And the child grew, and she brought him unto Pharaoh's daughter, and he became her son..."  (Old Testament | Exodus 2:9 - 10)

It seems apparent to me that Moses's parents had sufficient time to teach Moses about Jehovah and the covenants of his fathers.

I also thought it was interesting a dream that Moses's father had concerning Moses as recorded by Josephus -

“3. A man whose name was Amram, one of the nobler sort of the Hebrews, was afraid for his whole nation, lest it should fail, by the want of young men to be brought up hereafter, and was very uneasy at it, his wife being then with child, and he knew not what to do. Hereupon he betook himself to prayer to God; and entreated him to have compassion on those men who had nowise transgressed the laws of his worship, and to afford them deliverance from the miseries they at that time endured, and to render abortive their enemies’ hopes of the destruction of their nation. Accordingly God had mercy on him, and was moved by his supplication. He stood by him in his sleep, and exhorted him not to despair of his future favors. He said further, that he did not forget their piety towards him, and would always reward them for it, as he had formerly granted his favor to their forefathers, and made them increase from a few to so great a multitude. He put him in mind, that when Abraham was come alone out of Mesopotamia into Canaan, he had been made happy, not only in other respects, but that when his wife was at first barren, she was afterwards by him enabled to conceive seed, and bare him sons. That he left to Ismael and to his posterity the country of Arabia; as also to his sons by Ketura, Troglodytis; and to Isaac, Canaan. That by my assistance, said he, he did great exploits in war, which, unless you be yourselves impious, you must still remember. As for Jacob, he became well known to strangers also, by the greatness of that prosperity in which he lived, and left to his sons, who came into Egypt with no more than seventy souls, while you are now become above six hundred thousand. Know therefore that I shall provide for you all in common what is for your good, and particularly for thyself what shall make thee famous; for that child, out of dread of whose nativity the Egyptians have doomed the Israelite children to destruction, shall be this child of thine, and shall be concealed from those who watch to destroy him: and when he is brought up in a surprising way, he shall deliver the Hebrew nation from the distress they are under from the Egyptians. His memory shall be famous while the world lasts; and this not only among the Hebrews, but foreigners also:— all which shall be the effect of my favor to thee, and to thy posterity. He shall also have such a brother, that he shall himself obtain my priesthood, and his posterity shall have it after him to the end of the world.

“4. When the vision had informed him of these things, Amram awaked and told it to Jochebed who was his wife. And now the fear increased upon them on account of the prediction in Amram's dream; for they were under concern, not only for the child, but on account of the great happiness that was to come to him also. However, the mother's labor was such as afforded a confirmation to what was foretold by God; for it was not known to those that watched her, by the easiness of her pains, and because the throes of her delivery did not fall upon her with violence. And now they nourished the child at home privately for three months; but after that time Amram, fearing he should be discovered, and, by falling under the king's displeasure, both he and his child should perish, and so he should make the promise of God of none effect, he determined rather to trust the safety and care of the child to God, than to depend on his own concealment of him, which he looked upon as a thing uncertain, and whereby both the child, so privately to be nourished, and himself should be in imminent danger; but he believed that God would some way for certain procure the safety of the child, in order to secure the truth of his own predictions. When they had thus determined, they made an ark of bulrushes, after the manner of a cradle, and of a bigness sufficient for an infant to be laid in, without being too straitened: they then daubed it over with slime, which would naturally keep out the water from entering between the bulrushes, and put the infant into it, and setting it afloat upon the river, they left its preservation to God; so the river received the child, and carried him along. But Miriam, the child's sister, passed along upon the bank over against him, as her mother had bid her, to see whither the ark would be carried, where God demonstrated that human wisdom was nothing, but that the Supreme Being is able to do whatsoever he pleases: that those who, in order to their own security, condemn others to destruction, and use great endeavors about it, fail of their purpose; but that others are in a surprising manner preserved, and obtain a prosperous condition almost from the very midst of their calamities; those, I mean, whose dangers arise by the appointment of God. And, indeed, such a providence was exercised in the case of this child, as showed the power of God. (Antiquities of the Jews, Book 2, chapter 9, paragraph 3-4).