Wood and metal is often the preferred material for construction of various objects, but it's not the only option. Paper Maché (or Papier-mâché) is a great material for creating moulds for glass or other composites, and in some cases can be the material itself for various projects. The process goes back to ancient times, ancient Greece at least.
I've also used modelling clay or other modelling compounds, and dental amalgam. There are thermoplastics in sheet form that can also be used, and there are the casting plastics and polyurethanes (which have the advantage of being capable of almost any density or durometer rating). And of course there are the Room Temperature Vulcanizing (RTV) rubbers and silicones, and wet-moulded leather.
At least as far back as the 1970's commercial loudspeaker manufacturers were "doping" paper and plastic cones with kraft glue (the kind that goes on white and dries clear).
In college we made papers from various plant straws, old cotton clothing, and similar materials. Currency is usually made with flax straws and cotton; it's very durable. I once bought a wallet made in Japan of some kind of paper, it lasted me many years and wore very well.
You can make almost anything of any reasonable size if you really want to, without the use of metals or wood. But if you think a paper maché loudspeaker horn is "out there", there are people who make DIY vacuum tubes, complete with blown glass envelopes.