We present a full space inverse materials design (FSIMD) approach that fully automates the materials design for target physical properties without the need to provide the atomic composition, chemical stoichiometry, and crystal structure in advance. Here, we used density functional theory reference data to train a universal machine learning potential (UPot) and transfer learning to train a universal bulk modulus model (UBmod). Both UPot and UBmod were able to cover materials systems composed of any element among 42 elements. Interfaced with optimization algorithm and enhanced sampling, the FSIMD approach is applied to find the materials with the largest cohesive energy and the largest bulk modulus, respectively. NaCl-type ZrC was found to be the material with the largest cohesive energy. For bulk modulus, diamond was identified to have the largest value. The FSIMD approach is also applied to design materials with other multi-objective properties with accuracy limited principally by the amount, reliability, and diversity of the training data. The FSIMD approach provides a new way for inverse materials design with other functional properties for practical applications.