"HaShem spoke to Moshe and Aaron in the land of Egypt saying: This month is the beginning of your months; it will be the first of the months of your year." (Exodus 12:1-2)
This, the command to establish a calendar, is the first national mitzvah that God gave us. As the Ramban puts it: 
The command to establish a calendar is the first national mitzvah that God gave us.
"This is the first mitzvah that God commanded Israel through Moshe, which is why it says 'in the land of Egypt', because other mitzvot in the Torah were [given] at Mount Sinai.... And it would have been appropriate for Him to have started by saying, 'Speak to the entire congregation of Israel, saying: This month is the beginning of your months....' However, Moshe and Aaron take the place of Israel; and He said 'to you' [lachem - to you in plural, to all of you] connoting to all Israel throughout their generations. And He then said 'Speak to the entire congregation of Israel' (verse 3) when commanding them with the one-time mitzvah of taking the Egyptian Paschal Lamb on the tenth of the month."
On the Shabbat immediately before the month of Nissan (or Shabbat of Rosh Chodesh Nissan), we are commanded to read this mitzvah in the public Torah reading (Megillah 29b; Rambam, "Laws of Prayer" 13:20; Shulchan Aruch, Orach Chaim 685:4). "We read the section HaChodesh on the Shabbat immediately preceding Rosh Chodesh Nissan in order to sanctify the month of Nissan, as is written in the Torah, 'This month is the beginning of your months'." (Mishnah Berurah 685:1)
Previously, God had given specific mitzvot to individuals: Abraham was given the mitzvah of circumcision (Genesis 17:9-27), Isaac was commanded to take tithes (Genesis Rabbah 64:6; Rambam, "Laws of Kings" 9:1), Jacob was commanded not to eat the sinew of the hind-quarters of any animal (Genesis 32:25-33). But the mitzvah of determining the calendar was the first to be given to the Jewish nation as a whole.
The precise wording here is deeply significant: "This month is the beginning of your months (lachem - literally, 'to you'), it will be the first of the months of your year (rishon hu lachem - literally, 'it is the first to you')." The Torah emphasizes that this beginning of months, the calibrating of the calendar, is given over to us.
The Targum Yonatan's rendering makes this clear: "This month is yours to determine the beginning of months, and from it you will begin to count festivals and appointed times and seasons; it is the first for you for reckoning the months of the year."
There is a remarkable episode in the Mishnah (Rosh HaShanah 2:8):
On one occasion, there was a dispute whether or not to believe the witnesses who testified that they had seen the new moon. Rabban Gamliel, the Nasi (national leader and head of the Sanhedrin), accepted their testimony, while Rabbi Dosa ben Horkinus and Rabbi Yehoshua rejected it. The practical result was that according to Rabban Gamliel, the month began a day earlier than it did according to Rabbi Dosa ben Horkinus and Rabbi Yehoshua (who was the Av Beit Din or legal head of the Sanhedrin, subordinate only to the Nasi). What made this particularly sensitive was that this was the month of Tishrei; hence, this dispute influenced what day Yom Kippur (and the festivals) fell on.
Consequently, "Rabban Gamliel sent a message [to Rabbi Yehoshua]: 'I command you to come to me with your staff and your money on the day that Yom Kippur falls according to your calculation.' Rabbi Akiva went to him and found him distressed. He told him: 'I can learn that everything that Rabban Gamliel has done is appropriate, 
The origins of the Jewish calendar are on the fourth day of Creation.
because the Torah says, "These are the festivals of HaShem, holy convocations, that you will declare them." (Leviticus 23:4) Whether you declare them at their [expected] time or not at their [expected] time, these are the only festivals that I have.'" (Rosh HaShanah 2:9)
This is an astounding concept, which is worth examining.
The origins of the Jewish calendar are on the fourth day of Creation: "And God said: Let there be illuminations in the firmament of the Heavens, to distinguish between the day and the night, and to be as signs and for festivals and for days and for years." (Genesis 1:14) The Targum Yonatan renders: "...and they will be as signs, and for the times of the festivals, and according to them to calculate the days, and to sanctify the beginnings of the months [Rosh Chodesh], and the beginnings of the years [Rosh HaShanah] - when to intercalate an extra day in the months, and when to intercalate an extra month in the years...."
This has direct halachic consequences: the seasons, the months, the years, the festivals - all are determined according to the heavenly lights that God created for precisely this purpose. And yet, when the Sanhedrin passes a decree that the new moon will be visible on a specific day at a specific time, then that - and not their actual positions - is the determining factor.
In effect, God has given over to us - His children, His nation, His representatives in this world - the authority to determine how His creation continues.
He subsequently commanded us: "If a matter is too difficult for you to adjudicate, between blood and blood, between justice and justice, or between plague and plague - disputed words within your cities - then you will get up and ascend to the place that HaShem your God shall choose; then you will come to the Kohanim, the Levites, and to the judge who will be in those days. You will enquire, and they will tell you the matter of justice, and you will do according to the word that they will tell you." (Deuteronomy 17:8-10)
The Talmud (Rosh HaShanah 25b), addressing Rabban Gamliel's seemingly harsh behaviour towards Rabbi Yehoshua, picks up on the words "you will come to the Kohanim, the Levites, and to the judge who will be in those days": "Might you then imagine that someone would go to a judge who is not in his own days? [That is, the phrase 'who will be in those days' seems superfluous.] This teaches that it is only possible go to a judge in one's 
Rabbi Yehoshua was enjoined by the Torah itself to accept Rabban Gamliel's authority.
own days; and it is written (Ecclesiastes 7:10) 'Do not say, Why were the former days better than these?'" The inference is that Rabbi Yehoshua was enjoined by the Torah itself to accept Rabban Gamliel's authority.
Indeed, God has commanded us to accept the genuine Torah authorities in every generation. Rabbi Yehoshua was fully aware of this, "so he took his staff and his money in his hand, and went to Yavne, to Rabban Gamliel, on the day that Yom Kippur would have fallen according to his calculation." (Rosh HaShanah 2:9)
By commanding us to calibrate our calendar according to our own observations or - since the last Nasi, Hillel II (Hillel ben Rabbi Yehudah) fixed the permanent calendar in 4119 (359 BCE) - to follow the calculations of the Sanhedrin, God commanded us to become His partners in Creation.
This, then, is how the Nation of Israel begins its national mission. By sanctifying the first month, by subsequently sanctifying every month, by deciding precisely when each month and each year begins, we collectively become God's partners in Creation. And the logical conclusion is that by bringing about the final, complete redemption, we complete the history that He has decreed for this world.