looks too thin to cast a distance field shadow. you can override the distance field mesh to be thicker. you can use the distance field debug views to see what it looks like and if it is completely solid and encloses the head underneath.
if those are shadow maps the bias could be off or the distance of the lamp is too much and causes z-precision artefacts in the shadow depth map.
if this a singular outfit for the character you should bake a static shadow or occlusion texture or combine it with the diffuse map for the head. or make it a changeable “occlusion” texture incase it is an optional item.
I’m using MetaHumanSample project and noticed that mesh distance fields aren’t enabled by default in the project settings. After enabling them, the hat seems thick enough to cast a shadow.
However, when the light source has “Distance Field Shadows” enabled, there’s almost no shadow on the mesh. If I disable it, the shadow returns but looks odd.
I’ll investigate the static shadow next. Thanks for the help!