And his sister stood at a distance, to learn what would befall him (Exodus 2:4)
Why did Miriam stand at a distance? Rabbi Amram in the name of Rab said: Because Miriam prophesied, "My mother is destined to give birth to a son who will save Israel." When the house was flooded with light at the birth of Moses, her father arose and kissed her head and said: "My daughter, your prophecy has been fulfilled."
Exodus Rabbah 1:22