Q1 Why is such a precise time given?
Q2 why is such an imprecise place given?
' AND [God] SPOKE [UNTO MOSES] IN THE DESERT OF SINAI … ON THE FIRST DAY OF THE [SECOND] MONTH … [TAKE YE THE SUM OF ALL THE CONGREGATION] etc. – Because they were dear to him, God counts them every now and then: when they went forth from Egypt He counted them (exodus 12:37), when many of them fell in consequence of their having worshipped the golden calf He counted them to ascertain the number of those left (cf. Rashi Exodus 30:16); when he was about to make His Shechinah dwell amongst them (i.e. when He commanded them to make a Tabernacle), He again took their census; for on the first day of Nisan the Tabernacle was erected (exodus 40:2) and shortly afterwards, on the first day of Iyar, He counted them. (Rashi ad loc)
Raba taught that when people open themselves to everyone like a wilderness, God gives them the Torah (Babylonian Talmud Nedarim 55a.) Similarly, a Midrash taught that those who do not throw themselves open to all like a wilderness cannot acquire wisdom and Torah. The Sages inferred from Numbers 1:1 that the Torah was given to the accompaniment of fire, water, and wilderness. And the giving of the Torah was marked by these three features to show that as these are free to all people, so are the words of the Torah; as Isaiah 55:1 states, "everyone who thirsts, come for water." (Numbers Rabbah 1:7.)
Talmud Bavli Bava Batra 109b
Rava said, the verse said:... The father's family is considered family, but the mother's family is not considered family, as it says, 'by the clans of its ancestral houses, by their families, the homes of their fathers.'
The Gemara deduced from the words "by their families, by their fathers’ houses" in Numbers 1:2 that the Torah identifies families by the father's line. (see also B.Talmud Nazir 49a, Bekhorot 47a.)
Torah Temimah on BeMidbar 1 - why are women excluded from the census?
"The reason is simply because the men are those who construct the world and its civilization, and that's why males are called sons (banim) from the root of construction (binyan). (Baruch HaLevy Epstein)
Rabbi Phinehas the son of Idi noted that Numbers 1:2 says, “Lift up the head of all the congregation of the children of Israel,” not “Exalt the head” or “Magnify the head,” but “Lift up the head,” like a man who says to the executioner, “Take off the head of So-and-So.” Thus Numbers 1:2 conveys a hidden message with the expression “Lift up the head.” If the Israelites were worthy, they would rise to greatness, with the words “Lift up” having the same meaning as in Genesis 40:13 when it says (as Joseph interpreted the chief butler’s dream), “Pharaoh shall lift up your head, and restore you to your office.” If they were not worthy, they would all die, with the words “Lift up” having the same meaning as in Genesis 40:19 when it says (as Joseph interpreted the chief baker’s dream), “Pharaoh shall lift up your head from of you, and shall hang you on a tree.” (Gen. XL, 19).
note the verb -they "birthed" the community.
"How do we count and regard the people around us. Do we count them out of love? Do we count them by name, tied to families, their maternal or paternal lines? Who are the people who merit to be counted by us and why?" Dena Weiss