It is a mitzvah to construct the Tabernacle, as stated in Shemos 25:8.
וְעָ֥שׂוּ לִ֖י מִקְדָּ֑שׁ וְשָׁכַנְתִּ֖י בְּתוֹכָֽם׃
And let them make Me a sanctuary that I may dwell among them.
The Gemara (Temurah 31b) explains that the Mishkan- the Tabernacle, was constructed using the consecrated property:
“And let them make Me a sanctuary, that I may dwell among them” (Exodus 25:8). The verse indicates that the Tabernacle can be constructed from that which is Mine, i.e., consecrated property.
The Rambam, in his Moreh Nevuchim (3:32:2) uses the following words:
For this reason G-d allowed these kinds of service to continue; He transferred to His service that which had formerly served as a worship of created beings, and of things imaginary and unreal, and commanded us to serve Him in the same manner; viz., to build unto Him a temple; comp. "And they shall make unto me a sanctuary" (Exod. 25:8); to have the altar erected to His name; comp. "An altar of earth thou shalt make unto me" (ibid. 20:21); to offer the sacrifices to Him; comp. "If any man of you bring an offering unto the Lord" (Lev. 1:2), to bow down to Him and to burn incense before Him.
G-d instructs to build the Mishkan in Shemos 25:8. He uses the words "And let them make", e.g. let the people build the Mishkan, not "I will build the Mishkan". In a similair vein, the Ramban on Shemos 25:9 explains the words "so shall you make it"- this means that in future generations, when a vessel is lost, you know exactly how to remake it, since G-d gave these instructions:
AND SO SHALL YE MAKE IT — [also] “in future generations. If one of the vessels is lost, or when you make the vessels of the Sanctuary of Jerusalem, such as the tables, the candelabrums, the lavers, and the bases which Solomon made — after the pattern of these you shall make them
Rashi seems to accept this view:
according to all that I am showing you the pattern of the Tabernacle and the pattern of all its vessels, even so shall you make them.
The Chizkuni on Shemos 25:9 explains:
וכן תעשו, “and this is how you shall do it.” The letter ו at the beginning of the word וכן, is not necessary in this context; some commentators understand it as referring to what follows about the construction of the individual items of furniture for the Temple. The idea of the connective letter ו then would be: ”just as I instructed you first to build the structure, I will now instruct you to construct the furnishings to be housed in that structure.”
Also, I would like to add the commentary of the Siftei Chakhamim on the Rashi you quoted. On pasuk 25:32 he writes:
“Throw the mass into the fire.” This was done by Betzalel.
Elsewhere (v.33) he writes:
For they were unable to erect it . . . [Rashi knows this] because otherwise, they would not have brought it [to Moshe] in pieces, since it is the way of craftsmen to erect a house and then to show what they built. Therefore Rashi explains, “For they were unable to erect it.” Rashi then answers a further question: Every time they traveled from place to place, they erected the mishkon [themselves]. If so, why did they not do so now as well? Therefore Rashi explains, “Because Moshe did no work. . ..” Thus the first time, it was erected through Moshe, of its own. And from then on, each time they traveled, it stood upright on its own, and through those who erected it. (Nachalas Yaakov) Here it is implied that even Moshe erected it [only] by a miracle. But in Shabbos 92a, Berachos 54b and Bechoros 44a, it is implied that since Moshe was ten amohs tall, he therefore had the strength to erect it. See there.
On a side note, the Tosfos on the Gemara in Temurah 31b writes:
הא קדשי בדק הבית נותנין מנא ה"מ - תימה אלא מאי עבדינן מינייהו אי לא דיהבינן להו לאומנין בשכרן לחזק בדק הבית ואומר מורי הרמ"ר דס"ד דאין מותר לקנות אלא עצים ואבנים שהן צורך הבנין וקדושתן נשארה עליהן אבל ליתן לאומנין בשכרם להוציאן לחולין אסור אלא מתנדבין מעות בפני עצמן לפרוע לאומנין משום הכי איצטריך קרא דמאותן עצמן שהוקדשו נותנין לאומנין:
Rabbi Eliezer Chrysler of Kollel Iyun Hadaf, Yerushalayim in the "Tosfos-section" writes:
What else should one do with them, other than give it to the workers as remuneration for strengthening Bedek ha'Bayis?
Last, but not least, I would like to add-in the commentary of R'Moshe Feinstein on Shemos 25:8 (Darash Moshe al HaTorah, p. 133-134 ArtScroll)
On the surface it would appear that the holiness of the Sanctuary has to emanate from Hashem, and that humans can only build a physical structure which Hashem ten makes into a Sanctuary by causing His Presence to dwell in [...]. We must say that the Torah wishes to make the point that Hashem's explicit instructions apply only to creating this sanctity.
Personally, after reading the commentaries, I do not understand the statement of Rabeinu Yaakov mi'Lisa , G-d simply instructs the people to "make Me" a Tabernacle. Maybe if you could source that statement, we can look at "the bigger picture" of what R'Yaakov mi'Lisa writes, maybe he suggests a deeper meaning?
Klugman, E. M., Rohr, P. O., & Rosenberg, A. Y. (1994). Darash Moshe I: A selection of Rabbi Moshe Feinstein’s choice comments on the Torah (1st ed.). Mesorah Publications Ltd.