The potential of van der Waals (vdW) heterostructure to incorporate the outstanding features of stacked materials to meet a variety of application requirements has drawn considerable attention. Due to the unique quantum tunneling mechanisms, a type-III broken-gap obtained from vdW heterostructure is a promising design strategy for tunneling field-effect transistors. Herein, a unique Ga2O3/SiC vdW bilayer heterostructure with inherent type-III broken gap band alignment has been revealed through first-principles calculation. The underlying physical mechanism to form the broken gap band alignment is thoroughly studied. Due to the overlapping band structures, a tunneling window of 0.609 eV has been created, which enables the charges to tunnel from the VBM of the SiC layer to the CBM of the Ga2O3 layer and fulfills the required condition for band-to-band tunneling. External electric field and strain can be applied to tailor the electronic behavior of the bilayer heterostructure. Positive external electric field and compressive vertical strain enlarge the tunneling window and enhance the band-to-band tunneling (BTBT) scheme while negative electric field and tensile vertical strain shorten the BTBT window. Under external electric field as well as vertical and biaxial strain, the Ga2O3/SiC vdW hetero-bilayer maintains the type-III band alignment, revealing its capability to tolerate the external electric field and strain with resilience. All these results provide a compelling platform of the Ga2O3/SiC vdW bilayer to design high performance tunneling field effect transistor.