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Pharaoh issued an edict to kill all the Hebrew male babies. Moses was saved by his mother -- but how did Aaron slip through Pharaoh's net?
A key here can be found in Ex. 7:7 -
Moses was eighty years old and Aaron eighty-three when they spoke to Pharaoh.
So Aaron was three years older than Moses. We may say, then, that the edict to kill the male Hebrew babies was given AFTER Aaron's birth but before Moses'.
Alternatively, there is this from Exodus 1:17-20 --
The midwives, however, feared God and did not do what the king of Egypt had told them to do; they let the boys live. Then the king of Egypt summoned the midwives and asked them, "Why have you done this? Why have you let the boys live?" The midwives answered Pharaoh, "Hebrew women are not like Egyptian women; they are vigorous and give birth before the midwives arrive." So God was kind to the midwives and the people increased and became even more numerous.
Perhaps Aaron was one of those lucky boys who got past the original edict with the help of the midwives. (Note that in 1:22, Pharaoah re-issues the edict, this time to ALL of the people - since the midwives were apparently not getting the job done.)
Some may point to the formulation of this verse set, Ex. 2:1-2 --
Now a man of the house of Levi married a Levite woman, and she became pregnant and gave birth to a son. When she saw that he was a fine child, she hid him for three months.
Some may read this as saying that Moses was first-born, but since he has a sister who goes and looks after him (and is thus presumably older - Ex. 2:4ff), then 2:1-2 is a stylized introduction rather than, as we might perceive, an indication that Moses came first.