One of the most fundamental baryonic matter components of galaxies is the neutral atomic hydrogen (H I). At low redshifts, this component can be traced directly through the 21 cm transition, but to infer the H I gas content of the most distant galaxies, a viable tracer is needed. We here investigate the fidelity of the fine-structure transition of the (P-2(3/2) - P-2(1/3)) transition of singly ionized carbon C II at 158 mu m as a proxy for H I in a set simulated galaxies at z approximate to 6, following the work by Heintz et al. We select 11,125 star-forming galaxies from the SIMBA simulations, with far-infrared line emissions postprocessed and modeled within the SIGAME framework. We find a strong connection between C II and H I, with the relation between this C I relation (beta([C II])) being anticorrelated with the gas-phase metallicity of the simulated galaxies. We further use these simulations to make predictions for the total baryonic matter content of galaxies at z approximate to 6, and specifically the H I gas mass fraction. We find mean values of M-H I/M-* = 1.4 and M-H I/ M-bar,M-tot = 0.45. These results provide strong evidence for H I being the dominant baryonic matter component by mass in galaxies at z approximate to 6.