No. The largest possible square supported by the 43.27mm image circle common across the EF lens system is just under 30.6mm x 30.6mm. Anything bigger than that would result in corner shading.
The goal is not to get a perfect square output, but to get the maximum the image circle can produce. It's better to crop corner shading in post, than to crop a large fraction of the image circle with every shot.
Some EF lenses have a rectangular baffle, such as the 70-200, optimised for a 3:2 image format. This would allow for a theoretical maximum 24x24mm square sensor
Remove the baffle and stop producing lenses with such baffles. Do they serve any specific purpose which can't be accomplished with other features?
Many lenses have petal shaped hoods, optimised for a 3:2 image format. This again means a 24x24mm sensor Replace the hood. Plastic is cheap.
If using the DSLR format, the 44mm flange distance would be pushed over the limit to allow for a 36mm image height mirror - This was addressed in a previous post: this large sensor would either require a major redesign of the mirror assembly, or would need to wait for maturity of mirrorless.
