The clogging of the submerged entry nozzle (SEN) during the continuous casting of steel can be divided into two stages: the “early stage,” when the initial layer of the clog covers the SEN refractory surface owing to chemical reactions, and the “late stage,” when the clog layer continues to grow because of the deposition of non-metallic inclusions (NMIs). In this paper, a mathematical formulation is proposed for the build-up of the initial oxide. The chemical reaction mechanism is based on the work of Lee and Kang (Lee et al. in ISIJ Int 58:1257–1266, 2018): a reaction among SEN refractory constituents produces CO gas, which can re-oxidize the steel melt and consequently form an oxide layer on the SEN surface. The proposed formulation was further incorporated as a sub-model in a transient clogging model, which was previously developed by the current authors to track the late stage of clogging. The thermodynamics and kinetics of CO production, depending on the local pressure and temperature, must be considered for the sub-model of early-stage clogging. Test simulations based on a section of an actual industrial SEN were conducted, and it was verified that the clogging phenomenon is related to the SEN refractory, the chemical reaction with the steel melt, the local temperature and pressure, and the transport of NMIs by the turbulent melt flow in the SEN. The model was qualitatively validated through laboratory experiments. The uncertainty of some parameters that govern the reaction kinetics and permeability of the oxide layer is discussed.