AbstractInitial plant establishment is one of the most critical phases in ecosystem development, where an early suite of physical (environmental filtering), biological (seed limitation, species interactions) and stochastic factors may affect successional trajectories and rates. While functional traits are commonly used to study processes that influence plant community assembly in late successional communities, few studies have applied them to primary succession. The objective here was to determine the importance of these factors in shaping early plant community assembly on a glacial outwash plain, Skeiðarársandur, in SE Iceland using a trait based approach. We used data on vascular plant assemblages at two different spatial scales (community and neighborhood) sampled in 2005 and 2012, and compiled a dataset on seven functional traits linked to species dispersal abilities, establishment, and persistence for all species within these assemblages. Trait‐based null model analyses were used to determine the processes that influenced plant community assembly from the regional species pool into local communities, and to determine if the importance of these processes in community assembly was dependent on local environment or changed with time. On the community scale, for most traits, random processes dominated the assembly from the regional species pool. However, in some communities, there was evidence of non‐random assembly in relation to traits linked to species dispersal abilities, persistence, and establishment. On the neighborhood scale, assembly was mostly random. The relative importance of different processes varied spatially and temporally and the variation was linked to local soil conditions. While stochasticity dominated assembly patterns of our early successional communities, there was evidence of both seed limitation and environmental filtering. Our results indicated that as soil conditions improved, environmental constraints on assembly became weaker and the assembly became more dependent on species availability.