Identifying genomic signatures of natural selection can be challenging against a background of demographic changes such as bottlenecks and population expansions. Here, we disentangle the effects of demography from selection in the House Finch (Haemorhous mexicanus) using samples collected before and after a pathogen-induced selection event. Using ddRADseq, we genotyped over 18,000 SNPs across the genome in native pre-epizootic western US birds, introduced birds from Hawaii and the eastern United States, post-epizootic eastern birds, and western birds sampled across a similar time span. We found 14% and 7% reductions in nucleotide diversity, respectively, in Hawaiian and pre-epizootic eastern birds relative to pre-epizootic western birds, as well as elevated levels of linkage disequilibrium and other signatures of founder events. Despite finding numerous significant frequency shifts (outlier loci) between pre-epizootic native and introduced populations, we found no signal of reduced genetic diversity, elevated linkage disequilibrium, or outlier loci as a result of the epizootic. Simulations demonstrate that the proportion of outliers associated with founder events could be explained by genetic drift. This rare view of genetic evolution across time in an invasive species provides direct evidence that demographic shifts like founder events have genetic consequences more widespread across the genome than natural selection.