The calf was formed because the Israelites sought a replacement for Moses. His perceived delay in descending Mount Sinai caused them to fear they would be leaderless. The Sages add many details, not found in the verses, concerning different elements of this episode: the Israelites’ apprehension, Aaron’s role, Moses’ reaction, and Moses’ request for mercy on the children of Israel.

What is the meaning of what is written: “The people saw that Moses tarried [boshesh] in descending from the mountain” (Exodus 32:1)? Do not read boshesh; rather, read, ba’u shesh [meaning that six hours had passed]. Before Moses ascended to heaven to receive the Torah, he told the Israelites: I will return at the conclusion of forty days, at the beginning of the sixth hour from sunrise. At the conclusion of forty days, Satan came and brought confusion to the world so that the Israelites could not ascertain the precise hour. Satan said to the Israelites: Where is your master Moses? They said to him: He ascended to heaven. Satan said to them: Six hours have passed and he has yet to return. They ignored him. Satan said: He is dead. They ignored him. Satan showed them the image of [Moses dead on] a cot. That is the meaning of what they said to Aaron: “Because this [(Shabbat 89a; Pirkei deRabbi Eliezer 45)