I guess your objectives might need to be better defined. I'm tempted to give the standard "that depends"
answer, because your intended lifespan and immediate and long term use of the structure probably all inform your choices. In other words, your "cost function" or "loss function" needs to be better defined, or at least more clearly articulated. Many times, this measure of what is "optimal" changes as you plan and scheme and reconsider, so it, too, may be a moving target.
For example, if "fastest" is the
only thing that matters, a big wall tent might suffice. But, that's probably not really what you want, no matter if it can be set up in an afternoon.
If your "optimal" solution is more like "quickest to set up in the spring when the weather breaks, structurally substantial, and easily modified for future use", then maybe something like a timber framed structure would be a good choice. You could probably cut the frame this winter, possibly even assemble bents before the weather breaks, then raise the frame as soon as the foundation (whether concrete footer, dry laid stone, or a frost protected thickened edge slab) can bear the load in the spring. Infill choices abound: SIP (not very
permie, at least if made with plastic foam, but quick), cordwood, leichtlehm/clay-straw, wattle and daub (with or without additional insulation), compressed earth block (high strength adobe, Cinva ram style), true adobe, etc., etc. Temporarily, tarp in the sides, once the roof sheds water (even if just tar paper, synthetic roofing membrane or a blue tarp, until you can add the "real" roof). You can then work on infill out of the weather. You might be able to hasten the drying or curing schedule considerably for cob or daub and wattle infill early in the building season if the rain can be kept off, or work on making adobes out of the spring rains, or whatever. If you don't have access to lots of straight timbers for the frame, a cruck frame might be possible - this seems to have been a pretty common approach in Medieval England, though whether the crucks were preferentially selected or were the only timbers that people were permitted to use is an open question. Whatever the case, a few cruck frames built 700-800 years ago are still extant, and many more recently constructed, as well.
A lot of sand with a bit of clay sounds like a good recipe for rammed earth, compressed earth block, adobe or cob. If you have the sand, the lesser amount of clay might not be cost prohibitive, even if trucked in. Fast? Probably not the fastest, though the bricks (whether compressed or simply air/sun dried) could possibly be made up ahead of time (say, set up a
greenhouse to work in, which then becomes a true green house when the building
project is complete).
A yurt would go up pretty quickly, could be worked on over the winter (sew the cover, build the roof structure and outer wall lattice, maybe even put floor pieces together), and be warmer and more substantial than the wall tent.
A tipi probably doesn't meet your size requirements, but if speed of setup is the only objective, still might be a reasonable solution for a wintry climate. Though, I think it's in the Laubin book on tipis that they mention a large ceremonial double tipi with an oval floor plan. So, with an ozan (canvas partial ceiling), even that might work for you. I'll try to track down my copy and see if my "rememberer" is working properly!
A soddy is quite labor intensive, but might be climatically appropriate. There were (a few) two story sod houses built, and some rather impressive single story residences, as well. Done well, they lasted. Done poorly and in haste, they didn't endure very well. But, it is a natural building method, and with ample historical precedent. Lots of soddies were added on to, after the fact. I have some good documentation on soddy construction, also, especially as practiced historically in the Sandhills area of what is today Nebraska. Let me know if you are interested, I'll see if I can corral some of my resources.
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