Direct-injected (DI) compressed natural gas (CNG) engines are emerging as a promising technology for highly efficient and low-emission future engines. However, the design of direct injection systems for a compressible gas is challenging due to high Mach number flows and the occurrence of shocks. An outwardly-opening poppet-type valve design is widely used for DI-CNG. The formation of a hollow cone gas jet resulting from this configuration, its subsequent collapse, and mixing is challenging to characterize using experimental methods. Therefore, numerical simulations can be helpful to understand the process, and later to develop models for full engine simulations. In this paper, the results of high-fidelity Large-Eddy Simulation (LES) of a stand-alone injector are discussed to better understand the evolution of the hollow cone gas jet. The hollow cone gas jet is characterized in terms of several parameters such as axial penetration length, maximum jet width, area of jet, volume of jet, and mixing in terms of the mass-weighted probability density of the injected gas within the jet volume. Different grid resolutions have been used to study the effect on the gas jet behavior as well as mixing. The power-law scaling of the temporal evolution of the axial penetration length, the maximal width, and the area of the jet are compared with previously published literature for a similar hollow-cone injector. The applicability of different turbulence models commonly used in computationally cheaper Unsteady Reynolds Averaged Navier-Stokes (URANS) simulations is investigated. Both LES and URANS simulations over-predict the axial penetration length because of the initial non-linear behavior of the jet evolution. The reasons for this are investigated using URANS. It is found that the transient needle opening has a profound impact on initial stages of the gas jet formation and is responsible for the linear jet evolution observed in experiments. Moreover, the initial condition has a strong influence on later jet evolution in case of fixed needle simulations.