The interaction between a low-speed, zero-net-mass-flux (ZNMF) pulsatile air jet (Synthetic Jet, SJ) and a laminar boundary layer is investigated using Direct Numerical Simulations, with focus on the onset of transition to turbulence. This aspect is of crucial importance in industrial applications, when early transition to turbulence is required to reduce the extension of separated regions; the present investigation aims at providing useful information on the optimized design of fluidic devices for the laminar-turbulent transition control on aerodynamic surfaces. The influence of jet reduced frequency, momentum ratio, inlet Reynolds number and free stream turbulence (FST) on the control authority of the SJ has been evaluated. In most of the investigated cases the vortical structures generated by the interaction of the synthetic jet and the boundary layer are able to induce early transition to turbulence. In particular, it is found that increasing the momentum coefficient always reduces the size of the laminar region; on the other hand, a non-monotonic behaviour of the transition onset is found as the reduced frequency is increased, suggesting that an optimal value of the actuation frequency maximizing the anticipation of the transition region can be determined. Viscous diffusion completely annihilates any vortex motion for very low momentum ratios and high reduced frequencies. Finally, the control system is found to be robust with respect to FST, whose effect is to induce an instantaneous spanwise motion to the vortical structures in the far field, as suggested by the chaotic dynamics that can be observed within the physical domain