Conditional source-term estimation (CSE) is a novel chemical closure method for the simulation of turbulent combustion. It is less restrictive than flamelet-based models since no assumption is made regarding the combustion regime of the flame; moreover, it is computationally cheaper than conventional conditional moment closure (CMC) models. To date, CSE has only been applied for simulating canonical laboratory flames such as steady Bunsen burner flames. Industry-relevant problems pose the challenge of accurately modelling a transient ignition process in addition to involving complex domaingeometries. In this work, CSE is used to model combustion in a homogeneous-charge natural gas fuelled SI engine. The single cylinder Ricardo Hydra research engine studied here has a relatively simple chamber geometry which is represented by an axisymmetric mesh; moving-mesh simulations are conducted using the open-source computational fluid dynamics software, OpenFOAM. An oxygen-based reaction progress variable is employed as the conditioning variable, and its stochastic behaviour is approximated by the β probability density function (PDF). A trajectory generated low-dimensional manifold (TGLDM) has been used to generate tabulated chemistry described by reaction progress variable, temperature and pressure. The spark ignition process is modelled by placing a developed kernel profile of progress variable and temperature in order to match the experimentally-reported timing of 5% fuel mass fraction burn. Turbulent kinetic energy (k) and dissipation rate (ε) are estimated using transport equations; these are employed by the turbulence model and in the transport equations for calculating the mean and variance of progress-variable. CSE captures the behaviour of conditionally averaged temperature highlighting its drift from flamelet-governed behaviour during the early stages of kernel development. Estimates of pressure trace and pollutant emission trends obtained using CSE match experimental measurements satisfactorily. Despite the simplicity of models involved, the predictions obtained in this work demonstrate the capability of CSE as a turbulent combustion model for SI engines.