It's hard to fathom how an entire nation would truly believed that the 'golden calf' and not YHVH took them out of Egypt.

"And YHVH told Moses, come up to Me on the mountain... then Moses ascended YHVH's Mountain.  To the elders he said:  wait here for us until we return to you.  Behold, Aaron and Hur are with you, and should there be any problems, go to them."   (Ex 24:12-14)

 

Moses informed the elders that he was leaving 'until he returns', without specifying a date.  Even though we are told that Moses remained on the mountain for forty days (Ex 24:18) the people below had no idea how long Moses would be gone, neither did Moses or Aaron know in advance.  

 

This was not the first time that Moses ascended Mount Sinai to speak to YHVH.  (Ex 19:3,20; 24:1-2)  In previous ascents Moses was gone for no more than a day or two and Israel assumed that this time he would not be gone much longer. 

Days passed, weeks passed, yet Moses did not return. The last time they saw him, Moses had entered a cloud-covered mountain consumed in fire (Ex 24:17-18) so they concluded that Moses was dead. 

What could they do, return to Egypt?  Of course not!  That would be against YHVH's command.  Continue their journey to Canaan?  Why not!  Was this not the purpose of their exodus from Egypt - to inherit the Promised Land?   
 
Thus the Israelites approached Aaron, who Moses had left in charge (Ex 24:13-15) and asked for new leadership. 

"When the people saw that Moses was so long in coming down from the mountain, the people gathered on Aaron and said to him: Come make us an Elohim that will lead us towards the Promised Land because Moses, who took us out of the land of Egypt and promised to take us to Canaan, we do not know what has happened to him."  (Ex 32:1)

                               

They did not request a new god, but rather some one or thing that will "walk in front" and  lead them to the Promised Land.  This was understandable since YHVH promised to send a messenger to lead them and help them conquer the Land.

"Behold, I am sending a messenger before you to guard you and bring you to the place that I have made ready.  For My angel will go before you, and bring you to the Land."  (Ex 23:20-23) 

This was the last promise they heard before Moses ascended Mount Sinai, and now they demanded that Aaron provide them with a messenger in order that they may continue their journey to the Promised Land. 

"And Aaron said to them: Take off your gold... and bring them to me...  He took it from them and cast in a mold and made it into a molten calf...  this is your elohim/messenger who brought you out of the land of Egypt."  (Ex 32:2-4)

The people considered this "calf" as YHVH's agent, to lead them on their journey to the land of Canaan.  In their eyes, the calf was not a replacement but rather a representation of YHVH's Presence! 

To assure that the calf was properly understood, Aaron called for a celebration.

"Aaron built an altar in front of it (the calf), and Aaron called out and said:  A celebration for YHVH  tomorrow."  (Ex 32:5)

This 'celebration' paralleled the ceremony that took place at Mount Sinai forty days earlier, when Moses built an altar to YHVH. 

"They woke up early in the morning, and they built an altar at the foot of the mountain, twelve pillars (monuments) for the twelve tribes of Israel... and they offered burnt offerings and sacrificed peace offerings."  (Ex 24:4-5)

When Aaron made the calf he also built an altar to YHVH.

"They woke up early in the morning, after Aaron had built an altar in front of it (the calf), and they offered burnt offerings and sacrificed peace offerings."  (Ex 32:5-6)

               

Note the obvious parallels:  waking up early in the morning, building an altar in front of a 'symbol' representing their relationship with YHVH, offering burnt offerings and peace offerings, and 'eating and drinking' (compare Ex 24:11 with Ex 32:6).  Moses' ceremony included reading YHVH's Word - which most likely included the promise to send a messenger/angel to lead them. (Ex 23:20-23)  Not only were these two events parallel, they both related to Israel's acceptance of an intermidiary that will lead them to their promised land.  In both ceremonies an altar was erected in front of a symbol representing YHVH's promises.  Moses' altar had the twelve pillars, representing the Covenant with Abraham, while Aaron's altar had the golden calf, representing the Mount Sinai Covenant - a messenger to lead them.

Despite the many parallels, we find one additional phrase that is unique to the story of the golden calf.  

With Moses "They beheld YHVH and they ate and drank."   (Ex 24:11) 
With Aaron "They sat to eat and drink and they rose to play."  (Ex 32:6)

                                 

The word "play" is the key to understanding Israel's sin.  The simple translation means laughing or frivolous behavior, but it also refers to licentiousness and murder and implies more than just 'dancing'.  What began as a quiet ceremony turned into a 'wild party'. 

Notice Joshua's initial reaction to the 'loud noise' that he heard.  

"Joshua heard the sound of the people screaming loudly, and said to Moses:  there are sounds of war in the camp.  But Moses answered, these are not the sounds of triumph, nor are they the groans of defeat, they are sounds of wildness and frivolity that I hear."  (Ex 32:17-18)

 

The noise from this 'wild party' was so loud that it sounded to Joshua like a war was going on.

What provoked Moses to break the tablets was "He saw the calf and the dancing and became enraged."  (Ex 32:19)

Moses was more upset with the 'wild dancing' than by the calf itself.   YHVH became angry and told Moses to go down on the day AFTER Aaron made the calf.  (Ex 32:5-7)  If Israel's primary sin was making the golden calf, YHVH would have told Moses to go down on that very same day.  The fact that YHVH told him to go down on the next day, and only after "they rose up to play" points to it being the primary sin and not the golden calf.  

 

Even though the celebration around the calf began with good intentions, as a feast to YHVH - Ex 32:5, the people's behavior quickly became wild and out of control.  Once the drinking, dancing, and music began, the nation impulsively reverted back to their old ways, regressing back to their Egyptian culture.  Even though Israel was still immersed in Egyptian culture, YHVH took them out of Egypt in the hope that the miracles of the exodus and their experiences on the way to Mount Sinai would create a 'change of heart'.  When they arrived at Mount Sinai they proclaimed "we will do all that YHVH says and we will hear Him" (Ex 19:3-8 & 24:7) but they were not really ready to become YHVH's special nation yet.

 

The incident of the golden calf reflected the sad fact that despite the numerous miracles, deep down nothing had really changed. 

The Two stages of sin 

1.  Making a physical representation of ELOHIM. 

2.  The behavior at the conclusion of the ceremony. 
 

YHVH's 'double statement' to Moses addressed both stages.

(1) First statement - Ex 32:7-8

"And YHVH spoke to Moses: Hurry down, for your people have acted basely... they have turned astray from the way that I commanded them - they made molten calf as a representation of Me."

(2) Second statement - Ex 32:9-10

"And YHVH spoke to Moses:  I see this nation, behold it is a stiff necked people.  Now, allow Me, and I will kindle My anger against them and I will destroy them and I will  make you a great nation instead."

Note that "And YHVH said to Moses" is repeated twice even though Moses did not speak in between.

YHVH's first statement described the act that began with good intentions but was nonetheless forbidden.  (Exodus 20:4 - "Thou shall not make unto thee any graven image." )  This sin required rebuke and forgiveness (Ex 32:30) but was not severe enough to warrant the destruction of the entire nation.

YHVH's second statement addressed their "heart condition" - "they rose to play".  Because of their regression to the idolatrous Egyptian culture YHVH saw that they were a 'stiff-necked people' - unwilling to change their ways and concluded that they must be destroyed, choosing obedient and meek Moses to become His special nation instead.

These two levels are also found in the conversation between Moses and Aaron in the aftermath of this event.

"And Moses said to Aaron: What did this people do to you that caused you to bring upon them such a terrible sin?Aaron answered:  You know this people, that their ways are evil."  (Ex 32:21-22)

 

Moses knew that Aaron had no intention for the situation to get out of hand.  In fact, Aaron himself was not punished and later became the first High Priest of Israel.

"Moses 'saw' the people, that they were naked (wild and out of control) to their shame, when they got up to dance."   Ex 32:25

 

The two levels of punishment reflect the two stages of sin.  First, the three thousand 'instigators' who incited this incident were killed.  For them there was no forgiveness. (Ex 32:26-29)  However, on the second day, Moses asked YHVH to forgive the rest of the nation. (Ex 32:30-32)  Even though they had sinned, Moses hoped to secure a pardon because their actions began with 'good intentions'.  Moses received this pardon - but it wasn't so simple.

 

Delayed punishment or forgiveness

Even though YHVH agreed to Moses' first request (not to destroy the entire nation - Ex 32:11-14) his next request for forgiveness (in Ex 32:31-32) clearly indicated that the execution of the 3000 'instigators' did not absolve the rest of the nation, nor brought them forgiveness.  

"And YHVH told Moses: He who has sinned against Me shall be punished.  Now go lead the people to the place that I said, behold My angel will accompany you, and on the day that I will punish you, I will punish you."  (Ex 32:34)

 

YHVH instructed Moses to lead the Israelites to the Promised Land, thus fulfilling His covenant with Abraham, but He still planned to punish them later for the sin of the 'golden calf', at the time that He finds fit. 

Even though the Abrahamic Covenant  was fulfilled, the 'Sinai Covenant' - "I shall go with you" - remained 'broken'.

"YHVH said to Moses; Set out from here, you and the people that you have brought out of Egypt to the Land that I swore to Abraham, Isaac, and Jacob...  but I WILL NOT GO IN YOUR MIDST for you are a stiff-necked people, lest I destroy you on the journey."  (Ex 33:1-3)

 

YHVH was no longer personally with them.  This was reflected in His command that Israel remove their jewelry (a token of their betrothal) and Moses move his tent away from the camp, in order that YHVH could remain in contact with him.  (Ex 33:3-7)