While transcription factors (TFs) provide essential cues for directing and redirecting cell fate, TFs alone are insufficient to drive cells to adopt alternative fates. Rather, transcription factors rely on receptive cell states to induce novel identities. Cell state emerges from and is shaped by cellular history and the activity of diverse processes. Here, we define the cellular and molecular properties of a highly receptive state amenable to transcription factor-mediated direct conversion from fibroblasts to induced motor neurons. Using a well-defined model of direct conversion to a post-mitotic fate, we identify the highly proliferative, receptive state that transiently emerges during conversion. Through examining chromatin accessibility, histone marks, and nuclear features, we find that cells reprogram from a state characterized by global reductions in nuclear size and transcriptional activity. Supported by globally increased levels of H3K27me3, cells enter a quiescent-like state of reduced RNA metabolism and elevated expression of REST and p27, markers of quiescent neural stem cells. From this transient state, cells convert to neurons at high rates. Inhibition of Ezh2, the catalytic subunit of PRC2 that deposits H3K27me3, abolishes conversion. Our work offers a roadmap to identify global changes in cellular processes that define cells with different conversion potentials that may generalize to other cell-fate transitions.