Genomics is fundamentally changing epidemiological research. However, systematically exploring hypotheses in pathogen evolution requires new modeling tools. Models intertwining pathogen epidemiology and genomic evolution can help understand processes such as the emergence of novel pathogen genotypes with higher transmissibility or resistance to treatment. In this work, we present Opqua, a flexible simulation framework that explicitly links epidemiology to sequence evolution and selection. We use Opqua to study determinants of evolution across fitness valleys. We confirm that competition can limit evolution in high-transmission environments and find that low transmission, host mobility, and complex pathogen life cycles facilitate reaching new adaptive peaks through population bottlenecks and decoupling of selective pressures. The results show the potential of genomic epidemiological modeling as a tool in infectious disease research.