Inspired by aquatic creatures such as squid, the novel propulsion method based on pulsed jetting is a promising way to achieve high speed and high maneuverability for soft-body robots. Since these robots are often designed to operate in confined space with complicated boundary conditions, it is critical to understand their dynamics in the vicinity of solid boundaries. In this study we numerically examine the start maneuver of an idealized jet swimmer near a wall. Our simulations illustrate three important mechanisms: 1) Due to the blocking effect of the wall the pressure inside the body is affected so that the forward acceleration is increased during deflation and decreased during inflation; 2) The wall affects the internal flow so that the momentum flux at the nozzle and subsequently the thrust generation during the jetting phase are slightly increased; 3) the wall affects the wake so that the refilling phase is influenced, leading to a scenario in which part of the energy expended during jetting is recovered during refilling to increase forward acceleration and reduce power expenditure. In general, the second mechanism is weaker than the other two. The exact effects of these mechanisms depend on physical parameters such as the initial phase of the body deformation, the distance between the swimming body and the wall, and the Reynolds number.