We once discussed (link) the machlokes between Rashi and others as to whether building the Mishkan preceded the cheit ha’eigel or was a response to the cheit ha’eigel. The obvious difficulty with reading the Mishkan as a response to the cheit is that the discussion of the Mishkan in Parshas Terumah appears before the Torah tells us anything about the eigel. I want like to add one point to the discussion.
The gemara (cited by Rashi) tells us that Moshe first gave Bnei Yisrael the instructions of how to make the kelim for the Mishkan, but Betzalel figured out that this order cannot be correct – what good are kelim with no place to put them? First the building itself must be constructed, and afterwards the kelim that belong inside made and put in their proper place. Moshe responded that Betzalel had it right, and he must have been hiding in the shadows when Hashem gave the command (a play on the name Betzlalel, tzeil=shadow).
Why did Moshe himself did not give the command in the right order, first to build the building and then the kelim? Chasam Sofer explains that this was a test of Bnei Yisrael. Would they contribute for an aron which seems to have no place to be put? Would they contribute to make a menorah without knowing more about what it would be used for or where it would be placed? This was a test of “na’aseh v’nishma.”
The words “na’aseh v’nishma” don’t appear in the Torah before the aseres hadobros in Parshas Yisro; they appear at the very end of Parshas Mishpatim – right before Parshas Terumah. Might the command to build a Mishkan, the test of "na'aseh v'nishma," be deliberately placed here to juxtopose it to these words? I wouldn’t say that this alone justifies the order of the parshiyos according to Rashi, but it's something to think about.
On a different note, the issue of what comes first -- kelim or building -- I think speaks to a question of chinuch priorities. The sum total of what a ben Torah is more than the individual parts of learning, avodah, mussar, derech eretz. There is a "building" which contains all of those elements and gives them their proper place and balance. The catch-22 is that building has significance only because of the elements it contains. Without the persona of a ben Torah, learning is merely an intellectual exercise; yet without learning, how does one develop such a persona?