The replacement of hunter-gatherer lifestyles by agriculture represents a pivotal change in human history. The initial stage of this Neolithic transition in Europe was instigated by the migration of farmers from Anatolia and the Aegean basin. In this study, we modeled the expansion of Neolithic farmers into central Europe along the continental route of dispersal. We used spatially explicit simulations of paleogenomic diversity and high-quality paleogenomic data from 67 prehistoric individuals to assess how population dynamics between Indigenous European hunter-gatherers and incoming farmers varied across space and time. Our results demonstrate that admixture between the two groups increased locally over time at each stage of the Neolithic expansion along the continental route. We estimate that the effective population size of farmers was about five times that of hunter-gatherers. In addition, we infer that sporadic long-distance migrations of early farmers contributed to their rapid dispersal, while competitive interactions with hunter-gatherers were limited.