Contrail cirrus clouds are a major contributor to the climate impact of aviation. Large-scale models, such as general circulation models (GCMs) with an integrated contrail module, are used to estimate the radiative forcing of these clouds. However, small-scale processes cannot be explicitly resolved in these models and must therefore be parameterized. In this study, we develop a novel parameterization for the number of contrail ice crystals formed on ambient aerosols entrained into the exhaust plume behind aircraft burning hydrogen. The continuous entrainment of ambient aerosols, combined with higher supersaturation in hydrogen exhaust plumes, results in longer-lasting ice crystal formation than in conventional kerosene combustion, where ice crystals predominantly form on emitted soot. We construct the parameterization from a comprehensive database of time-resolved contrail formation simulations conducted with the Lagrangian Cloud Module in a box model approach. Shallow neural networks are used to reproduce the simulation outcome, complemented by analytical scaling relations to extend the applicability of the parameterization. The parameterization incorporates dependencies on ambient conditions, ambient aerosol properties and aircraft-related parameters. We compare the new parameterization with an existing one originally developed for conventional kerosene combustion that treats ice crystal formation as a single nucleation pulse. The comparison reveals that the assumption of a nucleation pulse is not reasonable for hydrogen combustion scenarios. We find it essential to base the parameterization on time-resolved simulations, as this realistically captures ice crystal formation on continuously entrained ambient aerosols.