Vermiculite is readily available at plant nurseries and garden stores, and withstands temperatures up to 1150°. But it comes as an aggregate of fragile, loose particles; to make a solid object out of it you need to stick them together somehow. The standard approach is to use sodium silicate, but I don’t have any.
Some adhesives are only activated by heat, and those would need a low-temperature adhesive to give the “green body” enough “green strength” to survive until firing. For many uses of vermiculite, much of the body would never reach a high enough temperature to activate it.
The most obvious such “adhesive” would of course be a hydrated clay, but low-temperature clays might slump too much at temperature.
Glassy carbon might be a useful, though weak, adhesive for this purpose; it won’t flux the vermiculite, won’t melt up to much higher temperatures, and can be easily made from sugar. You could tumble damp vermiculite particles in powdered sugar, or spray sugar water onto tumbling vermiculite, so that each particle is coated without penetrating much into its interior. Heat caramelizes the sugar into glassy carbon, hopefully without expanding the aggregate much. The sugar itself can serve as the initial adhesive if enough humidity is available and it is prevented from crystallizing. The greatest drawback of glassy carbon is that in an oxidizing atmosphere it erodes rapidly.
Superficial borax might also work: a thin coating of dissolved borax (31.7 g/ℓ) can dry and crystallize, providing green strength; upon heating, it will produce anhydrous borax at 75° and then boric-acid glass. This should eventually diffuse into the phyllosilicate vermiculite grains and eliminate the low-melting phase.
Soluble sodium donors also seem promising to apply in the same way: sodium hydroxide, carbonate, or bicarbonate on the surfaces of the grains should enable them to sinter together by forming a small amount of sodium silicate in situ. Trisodium phosphate might also work, perhaps forming silicon aluminum phosphates, though its aqueous solution might attack the vermiculite even at room temperature. Phosphates in general may be a useful way to increase the temperature the final mixture can handle, counteracting the fluxing effects of additives like boria and soda.
The most accessible alkali donor is probably wood ash, with its mixture of oxides and carbonates of sodium and potassium, which potters sometimes use for ash glazing.
(Some sodium hydroxide is currently crackling across the room from me as it releases its water of hydration in a pile of vermiculite on top of an electric burner; the temperature of the burner is plenty hot enough to completely melt it, but the vermiculite is slowing the process. Probably a more finely divided form, or a spray coating on the vermiculite granules, would have been better; both the vermiculite grains and the NaOH grains are about 3 mm.)
(The final result of that experiment: the sodium hydroxide apparently simply disappeared, leaving the vermiculite loose and not visibly changed.)
See also More cements for more notes on mineral cements that might be applicable.