We explore the impact of different forms of stochasticity on the expansion dynamics of a stochastic growth model called the $\infty$-parent spatial $Λ$-Fleming Viot process. This process belongs to a family of population genetics processes in a spatial continuum, and was recently introduced to study the evolution of genetic diversity in spatially expanding populations. Its stochastic reproduction dynamics gives rise to a rich growth structure, on which first theoretical results were obtained. In this paper, we further explore this growth dynamics using two complementary approaches: an analytical study of a simplified model for growth at the front edge, and a simulation-based study. We show that the observed expansion speed is the result of the interplay of stochasticity in shapes, timings and locations of reproduction events, each form of stochasticity being necessary but not sufficient to explain the expansion dynamics. We also identify distinctive scaling regimes for the variance of hitting times by the front and the bulk of the expansion. Moreover, we obtain results on the scaling of the front fluctuations, which point towards the front interface belonging to the KPZ universality class.