Moses was "placed outside" because of Pharaoh's command. This can be stated in active form. Alternate translation: "When his parents placed him outside" or "When they abandoned him" (See: [[rc://en/ta/man/jit/figs-activepassive]])
# Pharaoh's daughter ... raised him as her own son
She did for him every good thing a mother would do for her own son. Use your language's normal word for what a mother does to make sure her son becomes a healthy adult.
If your language has a word for an informal procedure, not a formal legal procedure, in which one family takes a child in and raises him, you may want to use that here. Pharaoh's daughter did do for Moses what any mother would do for her child, but this involved no formal legal procedure.