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Moshe is commanded to set up the Mishkan on Day 1, Month 1, Year 2 (Shemot 40)

Moshe is commanded to count the people on Day 1, Month 2, Year 2 (Bamidbar 1)

The half shekels from the census were used to make sockets and hooks for the Mishkan (Shemot 38:26)

In Shemot 12:37, an approximate figure for Exodus participants is given

Am I to assume that there was an actual but unmentioned census between the 1st and 14th of Nisan that also involved half shekels and this silver went to the (undecreed) Mishkan?

The Mishkan was traditionally completed Day 25 Month 9 Year 1 (25 Kislev) and was packed away before being set up on 1/1/2. Why did God wait after the Mishkan was set up to decree more silver was to be amassed? He could have had them perform the census on Purim (Day 15 Month 12) so they would have 2 weeks to gather the silver and make the sockets.

What am I missing?

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Rashi to Shemot 30:16 explains that there were two censuses.

The first census was conducted when they began donating towards the Mishkan, soon after Yom Kippur of the first year. The half-shekels from this census were then used to make the sockets of the Mishkan.

A further census was then conducted (after the Mishkan was inaugurated) at the beginning of the second month of the second year.

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