Jesus chose in His infinite wisdom, to begin His New Covenant on the Day of Pentecost, which the Jews know as Shavuot.

The Day of Pentecost was a fulfillment of what took place on Mount Sinai on the Day of Shavuot.

On Shavuot, God’s Law was written on tables of stone. (Exodus 24:12)  

On Pentecost God wrote His law on hearts. (Jeremiah 31:33)

On Shavuot the Jewish people accepted God's covenant and became His wife. (Exodus 19:7-8, Jeremiah 31:32)

On Pentecost those in the upper room accepted God's covenant and became His wife. (2 Corinthians 11:2, Ephesians 5:23-32)

On Shavuot the Jewish people became a peculiar treasure [special possession] from among all peoples, a kingdom of priests, and a holy nation. (Exodus 19:5-6)

On Pentecost New Covenant Believers became a peculiar people [“special possession”], a chosen generation [“a chosen people”], a royal priesthood, and a holy nation. (1 Peter 2:9)

On the Day of Pentecost the new Believers were all Jews. God had spoken to them through the Prophet Jeremiah that by entering His New Covenant they would continue to be His people. (Jeremiah 31:33)

"Behold, the days come, saith the LORD, that I will make a new covenant with the house of Israel, and with the house of Judah: Not according to the covenant that I made with their fathers in the day that I took them by the hand to bring them out of the land of Egypt; which my covenant they brake, although I was an husband unto them, saith the LORD: 

“But this shall be the covenant that I will make with the house of Israel; After those days, saith the LORD, I will put my law in their inward parts, and write it in their hearts; and will be their God, and they shall be my people.

"And they shall teach no more every man his neighbour, and every man his brother, saying, Know the LORD: for they shall all know me, from the least of them unto the greatest of them, saith the LORD: for I will forgive their iniquity, and I will remember their sin no more." - Jeremiah 31:31-34 KJV

Peter preached this new covenant message on the Day of Pentecost. 

"Then Peter said unto them, Repent, and be baptized every one of you in the name of Jesus Christ for the remission of sins, and ye shall receive the gift of the Holy Ghost." - Acts 2:38 KJV

Just as Jeremiah prophesied of the new covenant, by repentance and baptism in Jesus name God would “forgive their iniquity...and remember their sin no more.”

And by the gift of the Holy Ghost, as Jeremiah prophesied, “they shall all know me, from the least of them unto the greatest of them.”

As Peter preached, "But this is that which was spoken by the prophet Joel; And it shall come to pass in the last days, saith God, I will pour out of my Spirit upon all flesh: and your sons and your daughters shall prophesy, and your young men shall see visions, and your old men shall dream dreams: And on my servants and on my handmaidens I will pour out in those days of my Spirit; and they shall prophesy:" - Acts 2:16-18 KJV (Joel 2:28-29)

On the Day of Pentecost, Peter preached that the New Covenant would be not only to the Jews present that day, but extended to all nations, “to all that are afar off.” (Acts 10, Ephesians 2:11-18)

"For the promise is unto you, and to your children, and to all that are afar off, even as many as the Lord our God shall call." - Acts 2:39 KJV