Time of the Altar Dedication
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Hello
Indeed, as you calculated, all parts of the Tabernacle were ready in Kislev, and the Holy One, blessed be He, instructed to wait until the month of Nissan for the dedication of the Tabernacle, as He determined that this was the most appropriate time for its dedication.
And regarding this, our Sages said that the Holy One 'compensated' the month of Kislev by having the dedication of the renewed Temple in the days of the Hasmoneans occur in the month of Kislev, in exchange for the dedication of the Tabernacle which was postponed from Kislev to Nissan.
Source
Pesikta Rabbati (Piska 6 - And all the work was completed):
Rabbi Chanina said: On the 25th of Kislev, the work of the Tabernacle was completed, and it remained folded until the first of Nissan, when Moses erected it, as it is written: 'On the first day of the first month, you shall set up the Tabernacle of the Tent of Meeting' (Exodus 40:2), etc. The Holy One, blessed be He, said: 'I must compensate him,' and how did the Holy One, blessed be He, compensate him? With the dedication of the Hasmonean House.