We present an epitaxy-based approach for designing a 3C-SiC Capacitive Micromachined Ultrasonic Transducer (CMUT). The design requires to consider a 3C-SiC/Si/3C-SiC heterostructure on a Si substrate. This implies to address different growth steps of SiC on Si and Si on SiC. We present some specific growth related issued, namely the control of selectively grown Si on a masked SiC(100) and the further regrowth of 3C-SiC on a Si (110) layer. The final release of the SiC membrane, to define a CMUT, is also addressed using a simple thermal treatment allowing to suppress several technological steps.