Asymmetry in the spatially integrated, 1D H i global profiles of galaxies can inform us on both internal (e.g. outflows) and external (e.g. mergers, tidal interactions, ram pressure stripping) processes that shape galaxy evolution. Understanding which of these primarily drive H i profile asymmetry is of particular interest. In the lead-up to SKA pathfinder and SKA H i emission surveys, hydrodynamical simulations have proved to be a useful resource for such studies. Here we present the methodology behind, as well as first results, of ASymba: Asymmetries in H i of Simba galaxies, the first time this simulation suite has been used for this type of study. We generate mock observations of the H i content of these galaxies and calculate the profile asymmetries using three different methods. We find that $M_{\rm H\, {\small i}}$ has the strongest correlation with all asymmetry measures, with weaker correlations also found with the number of mergers a galaxy has undergone, and gas and galaxy rotation. We also find good agreement with the xGASS sample, in that galaxies with highly asymmetric profiles tend to have lower H i gas fractions than galaxies with symmetric profiles, and additionally find the same holds in sSFR parameter space. For low H i mass galaxies, it is difficult to distinguish between asymmetric and symmetric galaxies, but this becomes achievable in the high H i mass population. These results showcase the potential of ASymba and provide the groundwork for further studies, including comparison to upcoming large H i emission surveys.