Low background pressures are expected to be required in ITER for successful plasma breakdown. After plasma implantation, the particles released from plasma-facing components (PFCs) increase pressure in the main chamber, and it is therefore important to assess the expected timescales of post pulse fuel outgassing. This paper studies the reasons for different outgassing conditions in a large database of JET pulses obtained with a beryllium (Be) first wall (FW) and a tungsten (W) divertor, to estimate the minimum inter-pulse dwell time required in ITER. Outgassing is found to increase during the first few pulses of a day of operation in JET, due to increasing wall temperature and fuel inventory. The time evolution of experimental pressure curves is studied in a large dataset to identify general statistical trends. The code Migration of Hydrogen Isotopes in MaterialS (MHIMS) is then used to simulate a series of plasma discharges with inter-pulse outgassing in JET. The PFCs are modeled as reservoirs in Be, W and stainless steel. The results agree qualitatively with experimental pressure curves and the initial outgassing increase is reproduced. The MHIMS reservoir model is then extrapolated to ITER, adapting the simulation setup with larger surfaces, a different plasma background, and longer pulses. This analysis features a comparison between the use of Be and W as FW materials, with the latter being key in view of the 2024 ITER re-baseline, which eliminates Be in favor of W for the main chamber armor. After 30 min of inter-pulse outgassing, the hydrogenic pressure is 0.12–0.17 mPa with a Be FW. This value is reduced to 0.023–0.041 mPa when using a W FW, assuming no boronization. These pressures are much lower than the identified threshold of 0.5–1 mPa required for reliable ITER plasma start-up.