Actin is an intracellular protein that constitutes a primary component of the cellular cytoskeleton and is accordingly crucial for various cell functions. Actin assembles into semi-flexible filaments that cross-link to form higher order structures within the cytoskeleton. In turn, the actin cytoskeleton regulates cell shape, and participates in cell migration and division. A variety of theoretical models have been proposed to investigate actin dynamics across distinct scales, from the stochastic nature of protein and molecular motor dynamics to the deterministic macroscopic behavior of the cytoskeleton. Yet, the relationship between molecular-level actin processes and cellular-level actin network behavior remains understudied, where prior models do not holistically bridge the two scales together. In this work, we focus on the dynamics of the formation of a branched actin structure as observed at the leading edge of motile eukaryotic cells. We construct a minimal agent-based model for the microscale branching actin dynamics, and a deterministic partial differential equation (PDE) model for the macroscopic network growth and bulk diffusion. The microscale model is stochastic, as its dynamics are based on molecular level effects. The effective diffusion constant and reaction rates of the deterministic model are calculated from averaged simulations of the microscale model, using the mean displacement of the network front and characteristics of the actin network density. With this method, we design concrete metrics that connect phenomenological parameters in the reaction-diffusion system to the biochemical molecular rates typically measured experimentally. A parameter sensitivity analysis in the stochastic agent-based model shows that the effective diffusion and growth constants vary with branching parameters in a complementary way to ensure that the outward speed of the network remains fixed. These results suggest that perturbations to microscale rates can have significant consequences at the macroscopic level, and these should be taken into account when proposing continuum models of actin network dynamics.