Super Mario Bros 8 bits:

1 - First, buy a box of Lego Basic Parts, 325 pieces.

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2 - Use this image as a reference. Note that it is composed of equal size rectangles.

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3 - Each rectangle in the image above is a 4 pins Lego block . The box will have varying size Lego blocks, but by combining blocks of 2, 4, 6 and 8 pin gives you a way. Despite stocky, because the blocks are more horizontal than vertical, the result is cool :)

Are there enough pieces in the box to make it out of squares so it's the right proportion?

No, you will need two box, but I believe that will create a Super Mario too tall. Think this like a Mario before get the first mushroom.

Nice one sir! I love me some Legos and Mario.