Rashi in P’ VaYakhel writes that the pasuk “sheishes yamim ta’aseh melacha” teaches that the Mishkan can only be built during the 6 weekdays but not on Shabbos. Rashi’s interpretation is based on the Mechilta, which learns from this pasuk that even fixing the broken corner of a mizbeiach is prohibited on Shabbos.
According to most opinions of Tanaim (see Shabbos 87) the Torah was given on Shabbos, the 51st day after Pesach. The MG”A famously asks why we refer to the holiday of Shavuos, which we celebrate on the 50th day of the sefira count, as “zman mattan Toraseinu”, when the Torah was actually not given until the day after the holiday of Shavuos. You have until Shavuos to work out a good answer to that one, but for now, I want to focus on a different point. After working through the calculations of the dates, the Minchas Chinuch (#309) notes that Moshe was commanded to build a mizbeiach on the day before mattan Torah. If mattan Torah was on day 51 of sefira, the mizbeiach would have been built on day 50, which was the Yom Tov of Shavuos. How could Moshe violate the issur of building a mizbeiach on Yom Tov? True, the Torah had not yet been given, but Moshe, like the Avos, would certainly have observed halacha even before the formal mattan Torah.
The Minchas Yitzchak (Kuntres Divrei Cheifetz, end of vol 3) offers two answers: 1) the mizbeiach was not a permanent structure and therefore did not violate the d’oraysa prohibition of binyan; 2) two people worked on building the mizbeiach and each was “aino yachol” and therefore not in violation of a d’oraysa.
These answers each have debatable points, but I’ll leave that for another time. One final question worth thinking about: why is a limud necessary to teach us that building a Mishkan cannot be done on Shabbos? We know that a mitzvas aseh cannot be doche a lav + aseh, so why would we think that the Mishkan could be built on Shabbos? The Minchas Yitzchak has a beautiful pilpul to answer this question. I may try to post it later, but if I don’t get to it, it is worth the effort to look up.