Aaron and Hur had been left to look after the affairs of Israel while Moses was absent. Joshua, Moses' servant, had gone partway up the mountain with Moses, so he was not with the people at the time of this sin.
But while Moses was on the mountaintop speaking to God face to face, the people wanted some likeness to worship as a substitute.
The people were never allowed to see God face to face, but they knew He was on the mountaintop because of all the evidences they saw. But they wanted something they could feel with their hands, something they could see.
The religion of the natural man demands something he can perceive with his eyes. That is why so many people today--even Christians--go after things that are earthly. They need the security that is provided only by what they are able to touch and see.
The Israelites were no different; they wanted a god they could see. Moses was gone, and because their eyes had been on him rather than on God, they wanted an image.
Perhaps this is why God took Moses away from them for a time. God not only wanted to talk to Moses face to face, but He also wanted to reveal to the Israelites that they were not really trusting God as they thought they were.
What a lesson this is for believers today! Our trust should be in God, not in man.
"It is better to trust in the Lord than to put confidence in man" (Ps. 118:8).