Context. Understanding the connection between outflows, winds, accretion, and discs in the inner protostellar regions is crucial for comprehending star and planet formation processes. Aims. We aim to we explore the inner 300 au of the protostar IRAS 4A2 as part of the ALMA FAUST Large Program. Methods. We analysed the kinematical structures of SiO and CH₃OH emission with 50 au resolution. Results. The emission arises from three zones: (i) a very compact and unresolved region (< 50 au) dominated by the ice sublimation zone, at ±1.5 km s⁻¹ with respect to v_sys, traced by methanol; (ii) an intermediate region (between 50 au and 150 au) traced by both SiO and CH₃OH, between 2 and 6 km s⁻¹ with respect to v_sys, with an inverted velocity gradient (with respect to the large-scale emission), whose origin is not clear; (iii) an extended region (> 150 au) traced by SiO, above 7 km s⁻¹ with respect to v_sys, and dominated by the outflow. In the intermediate region, we estimated a CH₃OH/SiO abundance ratio of about 120–400 and a SiO/H₂ abundance of 10⁻⁸. We explored various possibilities to explain the origin of this region, such as, a rotating disc or inner envelope, a jet on the plane of the sky or precessing, and a wide-angle disc wind. Conclusions. We propose that CH₃OH and SiO in the inner 100 au probe the base of a wide-angle disc wind. The material accelerated in the wind crosses the plane of the sky, giving rise to the observed inverted velocity gradient, and sputtering the grain mantles and cores releasing CH₃OH and SiO. This is the first detection of a disc-wind candidate in SiO, and the second ever in CH₃OH.