Transcriptional variability facilitates stochastic cell diversification and can in turn underpin adaptation to stress or injury. We hypothesize that it may analogously facilitate progression of premalignancy to cancer. To investigate this, we initiated preleukemia in mouse cells with enhanced transcriptional variability due to conditional disruption of the histone lysine acetyltransferase gene Kat2a. By combining single-cell RNA sequencing of preleukemia with functional analysis of transformation, we show that Kat2a loss results in global variegation of cell identity and accumulation of preleukemic cells. Leukemia progression is subsequently facilitated by destabilization of ribosome biogenesis and protein synthesis, which confer a transient transformation advantage. The contribution of transcriptional variability to early cancer evolution reflects a generic role in promoting cell fate transitions, which, in the case of well-adapted malignancies, contrastingly differentiates and depletes cancer stem cells. That is, transcriptional variability confers forward momentum to cell fate systems, with differential multistage impact throughout cancer evolution.