GRB 170817A was a subluminous short gamma-ray burst detected about 1.74 s after the gravitational wave signal GW170817 from a binary neutron star (BNS) merger. It is now understood as an off-axis event powered by the cocoon of a relativistic jet pointing 15 to 30 degrees away from the direction of observation. The cocoon was energized by the interaction of the incipient jet with the non-relativistic baryon wind from the merger remnant, resulting in a structured outflow with a narrow core and broad wings. In this paper, we couple the observational constraints on the structured outflow with a model for the jet-wind interaction to constrain the intrinsic properties with which the jet was launched by the central engine, including its time delay from the merger event. Using wind prescriptions inspired by magnetized BNS merger simulations, we find that the jet was launched within about 0.4 s from the merger, implying that the 1.74 s observed delay was dominated by the fireball propagation up to the photospheric radius. We also constrain, for the first time for any gamma-ray burst, the jet opening angle at injection and set a lower limit to its asymptotic Lorentz factor. These findings suggest an initially Poynting-flux dominated jet, launched via electromagnetic processes. If the jet was powered by an accreting black hole, they also provide a significant constraint on the survival time of the metastable neutron star remnant.