I think some got caught up with seeing the word "cantilever" in your post and ignored the "non" part. (I almost did myself). So I assume you want, in simplest terms, a
platform with four legs that's tall enough to walk under? Just one single
platform? Anything else to attach to besides the two sets of stairs?
You could do a single 4x8
platform, but it won't be rock solid. I second Bill's dimensions that you should be aiming for a min of about 7'4 with a 6" frame for the
platform. You could go normal 2x4, but that leaves very little attachment area for the legs. A 2x6
leg into a 2x6 frame might flex a little, but not nearly as much as into a 2x4.
The cross bracing becomes the hard part if you want the area underneath completely walkable. Ideally you want 2 adjacent sides cross braced. If you need to keep all four sides open as possible my suggestion would be to use 3/4 ply to create corner blocks (just like making a
flat) that cross from the legs to the frame. You could possibly cut it in an arc shape for aesthetics and/or to maximize head room. I've used a full 8' long piece that extended the entire
platform and 4' down the legs and it works really well.
While you could get away with 4x8, I'd suggest doing 5x8 or 6x8, especially if you have multiple actors up there at once. Even with railings, being comfortable with your head 12-13 feet above the
ground is easier with a
bit more space to move. It also widens your footprint and makes the
unit more stable from tipping (since you can't anchor to the floor). Just note the bigger you go, the more you should increase the size of the 3/4 corner blocks.