Upon accepting God's covenant, Israel waited three days for God to appear at Mount Sinai.
Once Israel accepted GOD's covenant at Mount Sinai, GOD told them to prepare for His arrival three days from then.
10 Again the Lord said to Moses, “Go down and solemnly charge the people and sanctify them today and tomorrow, and let them wash their clothes. 11 Let them be ready for the third day, for on the third day the Lord will descend upon Mount Sinai in the sight of all the people. 12 You shall set bounds for the people all around, saying, ‘Take heed to yourselves that you do not go up to the mountain or touch its base. Whoever touches the mountain shall surely die. 13 Not a hand shall touch him, but he shall surely be stoned or shot with an arrow; whether man or beast, he shall not live.’ When the thunders, the trumpets, and the cloud depart from the mountain, they shall ascend the mountain.”
14 So Moses went down from the mountain to the people and sanctified them, and they washed their clothes. 15 Then he said to the people, “Be ready for the third day; do not come near your wives.”
(Exodus 19:10-15 OSB)
GOD wanted Israel to take His coming seriously, to take the covenant seriously.
The children of Israel had been immersed in Egyptian culture for hundreds of years. Egyptians had their own gods. By the time GOD sent Moses to deliver Israel, Israel had developed greater familiarity with Egyptian gods than they had of the God of their forefathers Abraham, Isaac, and Jacob.
Furthermore, GOD knew the heart of these people, collectively and individually. He knew their stubbornness and stiff-necked nature.
As He always does, GOD was giving these individuals every opportunity to be informed so that they could please Him. He knew He had to shock them and wake them up to appreciate the unique nature of Himself in relation to the gods of the nations.
Remember, these individuals had witnessed firsthand the amazing miraculous plagues GOD unleashed on Egypt—a fact that He reminded them of before offering Israel His covenant. These people had walked on dry ground in wonder as GOD parted the Red Sea into walls of water. And most recently, these people had witnessed GOD's faithfulness in their military conquest of Amalek who attacked them.
Despite all that they had seen and participated in, these individuals still frequently complained against Moses, Aaron, and GOD, wishing they had died in Egypt. What shortsightedness!
I believe it is for these reasons, among others, that GOD had them prepare and purify themselves for three days before His coming upon Mount Sinai.