In spatially heterogeneous environments, the processes of gene flow, mutation, and sexual reproduction generate local genetic variation and thus provide material for local adaptation. On the other hand, these processes interchange maladapted for adapted genes and so, in each case, the net influence may be to reduce local adaptation. Previous work has indicated that this is the case in stable populations, yet it is less clear how the factors play out during population growth, and in the face of temporal environmental stochasticity. We address this issue with a spatially explicit, stochastic model. We find that dispersal, mutation, and sexual reproduction can all accelerate local adaptation in growing populations, although their respective roles may depend on the genetic make-up of the founding population. All three processes reduce local adaptation, however, in the long term, that is when population growth becomes balanced by density-dependent competition. These relationships are qualitatively maintained, although quantitatively reduced, if the resources are locally ephemeral. Our results suggest that species with high levels of local adaptation within their ranges may not be the same species that harbor potential for rapid local adaptation during population expansion.