The applicability of wood-based, starch-bonded composite materials for three-dimensional (3D)-printed temporal, fully recyclable support structures was studied experimentally with respect to delivering the specific geometric and load-bearing features of the product of a continuous 3D concrete printing process. Extrudability of the support material developed was verified by direct test using a conventional screw extruder. The observations and quantitative results were compared with those gained with a ram extruder. The development of the compressive strength of the support materials was analyzed experimentally from an early age, beginning a few minutes after extrusion. The results obtained confirmed the sufficiency of the product’s strength in withstanding prospective weight loads of concrete layers printed on top of the support. Furthermore, methods of enhancing early-age compressive strength were analyzed, and a most promising approach was experimentally implemented—namely, the deposition of the material under a constant defined airflow. In contrast to its promising mechanical material characteristics, massive fungi formation was observed as early as 1 day, amounting to a severe drawback. Consequently, improvements to the material’s composition are suggested that will not impair the environmental sustainability of the support material.