G-d, through the help of Moses, rescued the children of Israel out of Bondage. G-d proved his strength and power through the ten plagues and helped them fight off the Egyptians by parting the Red Sea, yet after all this, the children of Israel still doubted G-d and built a golden calf to compensate, falling into a life of sin. This sin caused them to lose G-d's trust and plague his people.
When the people saw that Moses, who had went up the mount to retrieve the laws, had delayed from coming back, they made new gods so as to replace the G-d of Moses, proclaiming that "These be thy gods, O Israel, which have brought thee up out of the land of Egypt." These people, however, while in bondage, had faith in G-d, which had lasted for hundreds of years; All of their life, they had been raised to believe in one G-d, even though the Egyptians still believed in idols, including Moses. Yet, now that they were released from bondage, and Moses was taking longer than expected to climb a mountain, they decided now to lose faith, after the power of G-d had been shown to them, after their prayers had been answered. .
The fact that the people could lose faith so quickly is almost incomprehensible, and the question of why is not answered in the text, explained only by midrashic opinions. Verse one and verse two in chapter thirty-two leave almost no room for explanation, besides stating that they would make a god because they don't know what has become of Moses. However, it can be inferred that the children of Israel were not looking for a substitute for G-d, but instead a substitute for Moses from the lines "And the people saw that Moses was delayed in coming down .and they said [to Aaron]: Get up, make us a god.for this man, Moses, who has taken us out of the land of Egypt, we do not know what has become of him." Without Moses the people seemed lost, because they lost their leader, their deliverer, their voice of G-d.