Context. A low-mass companion to the two-solar mass star HIP 65426 has recently been detected by SPHERE at around 100 au from its host. Explaining the presence of super-Jovian planets at large separations, as revealed by direct imaging, is currently an open question. Aims. We want to derive statistical constraints on the mass and initial entropy of HIP 65426 b and to explore possible formation pathways of directly imaged objects within the core-accretion paradigm, focusing on HIP 65426 b. Methods. Constraints on the planet’s mass and post-formation entropy are derived from its age and luminosity combined with cooling models. For the first time, the results of population synthesis are also used to inform the results. Then a formation model that includes N-body dynamics with several embryos per disc is used to study possible formation histories and the properties of possible additional companions. Finally, the outcomes of two- and three-planet scattering in the post-disc phase are analysed, taking tides into account for small-pericentre orbits. Results. The mass of HIP 65426 b is found to be m_p = 9.9_−1.8^+1.1 M_J using the hot population and m_p = 10.9_−2.0^+1.4 M_J with the cold-nominal population. We find that core formation at small separations from the star followed by outward scattering and runaway accretion at a few hundred astronomical units succeeds in reproducing the mass and separation of HIP 65426 b. Alternatively, systems having two or more giant planets close enough to be on an unstable orbit at disc dispersal are likely to end up with one planet on a wide HIP 65426 b-like orbit with a relatively high eccentricity (≳ 0.5). Conclusions. If this scattering scenario explains its formation, HIP 65426 b is predicted to have a high eccentricity and to be accompanied by one or several roughly Jovian-mass planets at smaller semi-major axes, which also could have a high eccentricity. This could be tested by further direct-imaging as well as radial-velocity observations.