For what it’s worth, I didn’t have a case ready when mine arrived, but I did have an old (soft) Nintendo DS case (which I think was meant to support a DSi XL) that it ended up fitting in well. I don’t plan to use it as a long term solution, but if you have something like that laying around it could work.
Most reviews of it seem to list the dimensions, though they might be just the dimensions of the main board. Probably best to add a little extra for the plastics. And the depth doesn’t seem to be listed in these reviews, but I’d guess it’s about 25mm deep. 167x97mm is the size listed in all the articles (which presumably was part of the press release/kit). So it’s about 6.6"x3.8"x1". Go with 7"x4"x1" and you should be fine.