In many scientific and defense surveillance missions, reducing the size, weight, and power (SWaP) of sensing systems is critical to accomplishing the intended objectives. At the backend, compressive sensing (CS) has been widely adopted to maintain the signal fidelity with less measurements, thereby reducing the hardware complexity. On the other hand, SWaP reduction can also be achieved with intelligent mechanical design. In this paper, we discuss a novel system concept, namely, Underwater Inflatable Co-prime Sonar Array (UICSA), which provides SWaP compression on two fronts. First, the sonar array is implemented as an inflatable structure, also referred to as a deployable structure, which is a folded package with compact stowed dimension. The folded package can be detached from a carrying platform and it can morph into its final structure form at the destination. Second, a sparse array configuration, namely, a co-prime array, is employed, which can resolve a much higher number of sources compared to a conventional uniform half-wavelength spaced array for a given number of sensors. The integration of these two concepts leads to a simulatenous reduction in the stowed dimension of the sonar array and the number of employed hydrophones. We describe the development of a UICSA prototype and provide underwater source direction-of-arrival estimates obtained using initial datasets acquired with the developed prototype.