The production rate of charm quarks in strongly interacting matter is investigated under various conditions, employing the effective quasiparticle framework. This phenomenological approach treats quarks and gluons as quasiparticles with dynamically generated self-energies linked to the medium. This paper studies thermal production of charm quarks in hot deconfined matter when those quarks are treated as impurities with a constant mass or as dynamical quarks dressed by the effective mass. When charm quarks are considered quasiparticles, their large (compared to the bare value) mass generates a significant decrease in the production rate in the crossover region. Various initial conditions for the evolution of the system are applied, showing that lower initial temperature leads to the continual suppression of the charm quark production rate, which appears in line with the previously reported estimate at certain values of the initial parameters.