Re-posting this video again. I've tried it out and yeah, laminated cardboard with wheat paste totally works, the result is as strong as wood (and a little lighter.)
This is a near-perfect way to bootstrap structures and buildings. You can use waste cardboard, and wheat paste is incredibly cheap.
I want to try sodium silicate ("waterglass") as a glue, it should make the resulting material fireproof and as durable as stone.