Many materials for sure. Seconds to minutes is the difficult restriction.
If you can heat said material to deform it, it's called forging in the case of metals. Many polymers react the same way. Or if the material is molten then solidified, it's called casting.
Some alloys get harder by heat treatment, which may be fast if the part is thin. The treatment can be just heat, or quenching for some steels, or intense cold. Some alloys, known for rivets, are kept in a fridge up to forming, then ambient temperature hardens them; a bit more warmth would accelerate this.
Other materials can hold the given shape by a fast chemical reaction, for instance water absorption in quick-setting cement. Variants exist but their reaction speed is unclear to me; alumina powder is sold for the same way of use.
Some materials harden by baking, like clay. If thin enough, with a pre-heated oven, minutes seem within reach.
Some resins and glues harden within minutes or seconds. Give the resin a shape, let it harden. Or give some fibrous material a shape, impregnate with a resin, let harden. Mixing can start the reaction, or air humidity, or light, or adding a catalyst, and so on.
Dry sand can be poured, but if you compact it, it gets some resistance.
Some effects are a little bit more esoteric. Even pure water can freeze reversibly slightly above 0°C with the help of an electric field. Research labs certainly have materials usable at varied temperatures, and effects more exotic.
And so on and so forth. Many dozens more possibilities. Can you tell more?