In this paper, dynamic tritium flow rates and inventories of the outer fuel cycle (OFC) of a DEMOnstration nuclear fusion reactor (DEMO) are analyzed to determine the initial amount of tritium that has to be prepared to sustain plasma operation at reactor start-up, i.e., until tritium bred in blankets is extracted and available. The main components of the helium coolant ceramic reflector tritium breeding system were modeled in detail with the use of COMSOL Multiphysics and integrated into a system-level model within the MATLAB/Simulink platform to simulate OFC tritium streams. Furthermore, a control volume analysis was derived to incorporate the OFC flow rates calculated with the dynamic integrated numerical tool for initial start-up tritium inventory (ISTI) analysis. We found that the tritium processing time of the tritium extraction system (TES) plays a critical role for ISTI assessment. On one hand, for batchwise technology such as adsorption/regeneration columns, the OFC-attributed ISTI is ~2.6 kg calculated for a 3-GW fusion power reactor. On the other hand, online extraction techniques such as catalytic membrane reactors offer continuous operation and result in ~10 to 250 g of ISTI depending on the TES efficiency and breeder material tritium residence time. The helium coolant system (HCS) line has a minor impact on ISTI since tritium retention in HCS components is orders of magnitude lower than the TES line when a tungsten plasma-facing-component coating is implemented.