There are multiple similarities listed in the right hand column between Moses and Jesus. Our primary peek-a-boo into the matter is to see that the Exodus was a type and shadow of the Jewish Wedding all culminating in the expectation of our coming Bridegroom.
God authorized Moses to go on His behalf and fully communicate His intentions.
So I have come down to deliver them out of the hand of the Egyptians, and to bring them up from that land to a good and large land, to a land flowing with milk and honey…Come now, therefore, and I will send you to Pharaoh that you may bring My people, the children of Israel, out of Egypt. Ex 3:8-10
God pays the redemptive bridal price.
…but because the LORD loves you, and because He would keep the oath which He swore to your fathers, the LORD has brought you out with a mighty hand, and redeemed you from the house of bondage, from the hand of Pharaoh king of Egypt. Deut 7:8
They left with the plunder of Egypt.
And the LORD had given the people favor in the sight of the Egyptians, so that they granted them what they requested. Thus they plundered the Egyptians. Ex 12:36
Both Jews and Gentiles left Egypt.
A mixed multitude (God-fearing Gentiles) went up with them also, and flocks and herds—a great deal of livestock. Ex 12:38
As a side note, it was the mixed multitude (Gentiles) to first grumble and complain.
Eyrusin - Kiddushin – The Betrothal
They all passed through the waters of the Red Sea.
Moreover, brethren, I do not want you to be unaware that all our fathers were under the cloud, all passed through the sea, all were baptized into Moses in the cloud and in the sea, all ate the same spiritual food… 1 Cor 10:1-3
They dwelt under the cloud by day and a fire by night, The Lord’s Hoopah.
And the LORD went before them by day in a pillar of cloud to lead the way, and by night in a pillar of fire to give them light, so as to go by day and night. He did not take away the pillar of cloud by day or the pillar of fire by night from before the people. Ex 13:21, 22
The Katubah
Exactly fifty days after Passover, when they began their Exodus, they experienced Pentecost. God Himself came down to make His marriage vows, giving His very Word:\
You have seen what I did to the Egyptians, and how I bore you on eagles’ wings and brought you to Myself. Now therefore, if you will indeed obey My voice and keep My covenant, then you shall be a special treasure to Me above all people; for all the earth is Mine. And you shall be to Me a kingdom of priests and a holy nation. Ex 19:4-6
In Exodus 20, God began to speak His Word (which sounded like a trumpet) to Israel -- an extraordinary gift that has permanently changed our world! Unfortunately, the children of Israel broke their marriage vows right off the bat! So Moses went back up and made atonement on Mount Sinai again - interestingly enough on the very day of Yom Kippur, the Day of Atonement! When Moses came back down the mountain, he was veiled and a veil remains on Israel until the appointed time of unveiling.
Therefore, since we have such hope, we use great boldness of speech— unlike Moses, who put a veil over his face so that the children of Israel could not look steadily at the end of what was passing away. But their minds were blinded. For until this day the same veil remains uplifted in the reading of the Old Testament, because the veil is taken away in Christ. 2 Cor 3:12-14
Therefore, brethren, having boldness to enter the Holiest by the blood of Jesus, by a new and living way which He consecrated for us, through the veil, that is, His flesh… Heb 10:19, 20
For I do not desire, brethren, that you should be ignorant of this mystery, lest you should be wise in your own opinion, that blindness in part (veiled) has happened to Israel until the fullness of the Gentiles has come in. Rom 11:25
They began building the Tabernacle on the first day of the Feast of Tabernacles with great anticipation for the day when they would celebrate the fulfillment of God’s promises.
And let them make Me a sanctuary, that I may dwell among them. According to all that I show you, that is, the pattern of the tabernacle and the pattern of all its furnishings, just so you shall make it. Ex 25:8, 9