To gain insight into how an adjuvant impacts vaccination responses, we use systems immunology to study human H5N1 influenza vaccination with or without the adjuvant AS03, longitudinally assessing 14 time points including multiple time points within the first day after prime and boost. We develop an unsupervised computational framework to discover high-dimensional response patterns, which uncover adjuvant- and immunogenicity-associated early response dynamics, including some that differ post prime versus boost. With or without adjuvant, some vaccine-induced transcriptional patterns persist to at least 100 days after initial vaccination. Single-cell profiling of surface proteins, transcriptomes, and chromatin accessibility implicates transcription factors in the erythroblast-transformation-specific (ETS) family as shaping these long-lasting signatures, primarily in classical monocytes but also in CD8+ naive-like T cells. These cell-type-specific signatures are elevated at baseline in high-antibody responders in an independent vaccination cohort, suggesting that antigen-agnostic baseline immune states can be modulated by vaccine antigens alone to enhance future responses.