An additive manufacturing method and machine for an object using at least one powder, capable of limiting risks of dissemination of the powder. The method including the following steps in succession: manufacture a solid block starting from the powder and a sublimatable material, load the solid block in a loading space of the machine; sublimate the material present in the solid block and recover the powder; and additive manufacturing of the object by stacking successive layers made using the powder recovered in the previous step.