God himself chose the date for the organization of the church. Read more about the account below:
"Early in April 1830 the young prophet received the revelation that has become section 20 of the book called the Doctrine and Covenants. It is often referred to as a “revelation on Church organization and government.” Of this, the Prophet Joseph wrote: “We obtained of him [Jesus Christ] the following, by the spirit of prophecy and revelation; which not only gave us much information, but also pointed out to us the precise day upon which, according to his will and commandment, we should proceed to organize his Church once more here upon the earth.”
The first verse of the revelation reads: “The rise of the Church of Christ in these last days, being one thousand eight hundred and thirty years since the coming of our Lord and Savior Jesus Christ in the flesh, it being regularly organized and established agreeable to the laws of our country, by the will and commandments of God, in the fourth month, and on the sixth day of the month which is called April.” [D&C 20:1]
One cannot study this revelation without being tremendously impressed with the knowledge and understanding the Lord of heaven poured out upon his servant concerning the matters vital to the salvation of man and the reestablishing of the kingdom of God upon the earth." (April 6, 1830: The Day the Church was Organized, link below)
Additionally, here is a quote from the article that says one part of what happened that day-
“the Holy Ghost was poured out upon us to a very great degree—some prophesied, whilst we all praised the Lord, and rejoiced exceedingly.”
This is God's true church on this earth today, organized by his command and with him as its head.
It began with only 6 members, and it now numbers over 15 million today. In scripture we are promised it will never again be taken from the earth, and is that Great Stone cut without hands that will roll forth throughout the Earth.
As Elder Packer said, The mind of man cannot conceive [the scope and magnitude] of this Latter Day work. What began that day in 1830 will continue until Christ the Lord presents the kingdom complete to his Father, and says, "The Work is Done."
We are the recipients of these great blessings. Eternal life and exaltation for us, our ancestors, our posterity, our families, and all of the family of man who come unto Christ will be the recipients of the blessings of heaven.
May we ever be grateful for that.
I urge you to follow the links to read the powerful accounts and articles about the restoration of the Church in our day.
More discussing what happened that sacred day can be found at https://www.lds.org/ensign/1971/01/april-6-1830-the-day-the-church-was-organized
The section upon which the organization of the church was predicated can be found at https://www.lds.org/scriptures/dc-testament/dc/20
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Picture is organization of the church by Barrett