It was 3 days from the arrival at Sinai to law-giving. (19:11)
1 day later the blood of the covenant was sprinkled on the people (24:4)
6 days after that Moses enters the glory cloud on top of the mountain (24:16)
For 40 days Moses receives the instructions for the tabernacle (24:18)
So when Moses descends the mountain we have a kind of a Pentecost - a 50th day.
But it's a reverse-Pentecost. The nations are repulsed (32:25). 3000 people die (v28), cf Acts 2:41). And all because they didn't wait for the LORD (v1, cf Acts 1:4).
The people have always wanted (and needed) someone to go before them. The Unseen LORD had promised His Divine Angel to fight at their head (23:20ff). He was the One who had commissioned Moses (3:2) and brought them out of slavery (14:19) on eagles wings (19:4) to serve God Most High (3:12). Moses and the elders have seen Him and eaten with Him (24:9ff). Yet He obviously wasn't moving according to the people's timetable. So in impatience they settle for counterfeits - a religious substitute for Christ. (Notice the same sin again in 1 Samuel 8:20 - this time the Israelites seek a political substitute for Christ - one 'to go before them').
In contrast to the free and liberal giving for the tabernacle, Aaron demands offerings for his false gods (v2). False religion is always compelled, true worship of the LORD is always free.
The plunder from the Egyptians (3:22; 12:36), instead of being pressed into the LORD's service, is made into a golden calf. But this is idolatry no matter how much the LORD's name is invoked (v5).
Why a calf? Well Psalm 106:19-20 clarifies that this is the calf of an ox. Now when you put Ezekiel 1:10 and 10:14 together you see that cherubs are like oxen. And we all know who the guardian cherub is (Ezekiel 28:14ff). Here is worship of Satan! Within a month of being sprinkled by the blood of the covenant and solemnly vowing to uphold it, while Moses is on the brooding fiery mountain with God Most High, here they are worshipping the devil. Notice how "the LORD" is invoked in their Satan worship - a salutary lesson that not everyone who says "Lord, Lord" is truly serving Him!
These people deserve the burning wrath of the LORD out of the heavens (v10; cf Gen 19:24). But just as Moses had interceded for wicked Pharaoh (e.g. 8:8) now he intercedes for wicked Israel. The LORD had called Israel "your people" (v7), Moses responds to the LORD - they are "your people" (v11) and implores the LORD to turn (shub) from wrath and have compassion (naham) (v12). The LORD does indeed have compassion / is sorry but this is not the end of the matter.
Moses descends the mountain with the same burning anger as the LORD Himself (v19).
Through the priests he executes a judgement on the people - this is the Levites' ordination! (v29) They have always been blood-thirsty men: "their swords are weapons of violence." (Gen 49:5) When you came to a Levite to confess your sin, you were coming to a violent man with a sword. As he plunged that sword into the animal substitute you would be left in no doubt that this blood-shed is precisely what you deserved.
But even after this blood-shed, Moses realises there's still a work of atonement to be performed:
I will go up to the LORD; perhaps I can make atonement for your sin. (v30)
Here's what he offers to the Father:
Blot me out of the book you have written. (v32)
He doesn't offer the blood of goats or bulls, he doesn't offer the blood of the guilty. He offers his own blood - the blood of the innocent, the blood of a Levite, the blood of the people's ruler.
Would Moses himself be the promised Lamb to be provided on the mountain to make atonement? Genesis 22:1-14 has been promising just this atonement for centuries - the Lamb on the mountain as a burnt offering. And Abraham is certainly on Moses' mind (v13). Would Moses be the One to make atonement?
No. God Most High declines Moses' offer. Instead He reminds him of His Angel - the true leader of the people (v34). The true Warrior and Commander at their head was indeed going before them. They must continue to wait for Him and to trust in Him.
One day He would descend from the heavenlies, the Divine Angel and Saviour, an Intercessor for the people, a Priest in the order of Melchizedek, the Ruler of rulers and a true Innocent. He would be handed over to death by Levites, killed by piercings and blotted out of the Father's book. And right there in bloody sacrifice the true God is on show for the whole world. Not a golden calf. More of a bronze serpent. But this is the real God. Every other god is a counterfeit.