The population of giant planets on wide orbits around low-mass M dwarf stars is poorly understood. However, the discovery and characterization of these planets is key to understanding the architectures and evolution of M dwarf planetary systems, and it places their frequent and potentially habitable inner planets in context. While current ground-based imaging struggles to probe below a Jupiter mass at large separations, the unprecedented sensitivity of JWST NIRCam coronagraphic imaging provides direct access to planets significantly less massive than Jupiter beyond 10 AU around the closest, youngest M dwarfs. We present the survey design, observations, and preliminary results of JWST GTO Program 1184, a NIRCam coronagraphic imaging survey of very nearby and young low-mass stars.