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How drug-tolerant persister (DTP) cells escape quiescence to drive tumour relapse remains a central unresolved question in cancer evolution. Here, we use neuroblastoma and hepatoblastoma, paediatric cancers with low genetic instability, as tractable model systems to study the principles and molecular mechanisms key in the early stages of adaptation to treatment. We identify transcriptional noise, the stochastic variability in gene expression, as a latent cellular property amplified post-treatment, during awakening from persistence, which drives adaptive regrowth following therapy withdrawal. Through functional assays, lineage tracing and single-cell multiomics, we show that treatment enriches for progenitor-like tolerant states with limited detectable clonal selection. Upon drug withdrawal, awakening proceeds via a stochastic process driven by noise-enabled plasticity in cell identity programmes. Mechanistically, AP-1-bound chromatin states emerge post-treatment, and AP-1 activity primes KDM5A recruitment to cell-state identity genes during awakening, driving H3K4me3 peak narrowing at their promoters and an increase in transcriptional noise that enables MES-to-ADRN plasticity. Pharmacological or genetic inhibition of AP-1 or KDM5 activity suppresses transcriptional noise and phenotypic plasticity, blocks DTP exit and prevents tumour recovery in both neuroblastoma and hepatoblastoma models. Together, these results identify KDM5-mediated transcriptional noise, operating within AP-engaged chromatin landscapes, as a key driver of early adaptation to treatment. Targeting this axis offers a strategy to exploit DTP awakening as an evolutionary bottleneck to prevent treatment adaptation and cancer relapse. GRAPHICAL ABSTRACT