We analyze ice crystal formation behind future hydrogen fuel cell-propelled aircraft via simulations using the particle-based Lagrangian Cloud Module (LCM) in a box model approach. Unlike conventional kerosene combustion, the exhaust of these aircraft could be significantly more humid and contain no soot particles, resulting in larger supersaturation values during plume cooling. These conditions can promote water droplet formation via Homogeneous Droplet Nucleation (HDN), which may substantially increase the number of contrail ice crystals. We implement the HDN into the LCM box model and validate the implementation against benchmark cases from the International Wet Steam Modeling Project. For the first time, the impact of HDN on ice crystal number in nascent contrails is quantified for exhaust parameters representative of fuel cell-propelled aircraft. We demonstrate that a low exhaust temperature together with high exhaust humidity leads to a large increase in ice crystal numbers due to additional droplet formation via HDN and their subsequent freezing. This would amplify the climate-forcing potential of an individual contrail. Conversely, reducing water vapour emissions suppresses HDN and effectively reduces the ice crystal number. The increase in ice crystal numbers is higher in cold ambient conditions <em>T</em>_amb ⪅ 218 K, which are, however, not expected to occur often on low flight levels of propeller aircraft. A sensitivity analysis reveals that faster plume dilution can lead to an increase of ice crystal number by orders of magnitude through an increased HDN rate. We propose that the slope <em>G</em> of the mixing line, which describes the thermodynamical conditions of the diluting plume, should be kept below around <em>G</em> &lt; 10 Pa K^&minus;1 by technical means to ensure that HDN does not occur, regardless of the ambient conditions.