The fraction of stars in binary systems within star clusters is important for their evolution, but what proportion of binaries form by dynamical processes after initial stellar accretion remains unknown. In previous work, we showed that dynamical interactions alone produced too few low-mass binaries compared to observations. We therefore implement an initial population of binaries in the coupled magnetohydrodynamics and direct N-body star cluster formation code torch. We compare simulations with, and without, initial binary populations and follow the dynamical evolution of the binary population in both sets of simulations, finding that both dynamical formation and destruction of binaries take place. Even in the first few million years of star formation, we find that an initial population of binaries is needed at all masses to reproduce observed binary fractions for binaries with mass ratios above the q ≥ 0.1 detection limit. Our simulations also indicate that dynamical interactions in the presence of gas during cluster formation modify the initial distributions towards binaries with smaller primary masses, larger mass ratios, smaller semimajor axes and larger eccentricities. Systems formed dynamically do not have the same properties as the initial systems, and systems formed dynamically in the presence of an initial population of binaries differ from those formed in simulations with single stars only. Dynamical interactions during the earliest stages of star cluster formation are important for determining the properties of binary star systems.