Inherent properties of superconducting Bi₂Sr₂CaCu₂O_8+x films, such as the high superconducting transition temperature T_c, efficient Josephson coupling between neighboring CuO layers, and fast quasiparticle relaxation dynamics, make them a promising platform for advances in quantum computing and communication technologies. However, preserving two-dimensional superconductivity during device fabrication is an outstanding experimental challenge because of the fast degradation of the superconducting properties of two-dimensional flakes when they are exposed to moisture, organic solvents, and heat. Herein, to realize superconducting devices utilizing two-dimensional (2D) superconducting films, we develop a novel fabrication technique relying on the cryogenic dry transfer of printable circuits embedded into a silicon nitride membrane. This approach separates the circuit fabrication stage requiring chemically reactive substances and ionizing physical processes from the creation of the thin superconducting structures. Apart from providing electrical contacts in a single transfer step, the membrane encapsulates the surface of the crystal, shielding it from the environment. The fabricated atomically thin Bi₂Sr₂CaCu₂O_8+x-based devices show a high superconducting transition temperature of T_c ≃ 91 K close to that of the bulk crystal and demonstrate stable superconducting properties.