Cancer initiation has traditionally been explained by the progressive accumulation of somatic genetic alterations. Although this paradigm remains fundamental, increasing evidence indicates that long-term biological exposures including chronic inflammation, metabolic dysfunction, oxidative stress, mitochondrial adaptation, and immune dysregulation can produce persistent regulatory changes that are not fully explained by DNA sequence variation alone. Existing concepts such as epigenetic memory, metabolic memory, trained immunity, and adaptive cellular plasticity each describe important aspects of biological persistence but do not provide an integrated framework explaining how prolonged exposure histories may influence future oncogenic susceptibility. Here, we propose temporal genomic memory (TGM) as a testable systems biology framework describing how sustained biological experiences may be progressively integrated, compressed, and retained as persistent regulatory states through coordinated interactions among metabolic signaling, mitochondrial function, chromatin remodeling, regulatory RNA networks, and tissue-level immune adaptation. Unlike existing memory paradigms that primarily emphasize individual regulatory mechanisms, the proposed framework introduces regulatory compression as a conceptual process through which diverse biological signals are consolidated into latent molecular configurations capable of influencing future transcriptional responsiveness. Under permissive conditions such as aging, chronic inflammation, immune decline, or recurrent metabolic stress, these latent regulatory states may undergo molecular recall, thereby modifying cellular responses to subsequent biological challenges and potentially increasing oncogenic susceptibility in cooperation with established genetic and environmental factors. A conceptual mathematical representation is introduced to describe biological signal accumulation, regulatory compression, and recall activation while emphasizing its heuristic rather than predictive purpose. We further propose experimentally testable strategies based on chronic exposure, stress-withdrawal persistence, recall-challenge paradigms, and integrated multi-omics analyses to evaluate the hypothesis. Temporal genomic memory is not intended to replace the somatic mutation theory of cancer. Instead, it provides a complementary systems-level perspective integrating metabolic history, mitochondrial signaling, epigenetic regulation, and persistent transcriptional adaptation into a unified theoretical framework for investigating long-latency cancer initiation.