Coronaviruses (CoVs) encode 16 nonstructural proteins (nsps), most of which form the replication–transcription complex (RTC). The RTC contains a core composed of one nsp12 RNA-dependent RNA polymerase (RdRp), two nsp8s, and one nsp7. The core RTC recruits other nsps to synthesize all viral RNAs within the infected cell. While essential for viral replication, the mechanism by which the core RTC assembles into a processive polymerase remains poorly understood. We show that the core RTC preferentially assembles by first having nsp12-polymerase bind to the RNA template, followed by the subsequent association of nsp7 and nsp8. Once assembled on the RNA template, the core RTC requires hundreds of seconds to undergo a conformational change that enables processive elongation. In the absence of RNA, the (apo-)RTC requires several hours to adopt its elongation-competent conformation. We propose that this obligatory activation step facilitates the recruitment of additional nsps essential for efficient viral RNA synthesis and may represent a promising target for therapeutic interventions.