No it won't; not with all else being equal. A larger sensor camera has to do more magnification to achieve identical framing on the same subject, thus getting shallower depth of field. A medium-format camera such as a Fujifilm GFX series would do worse still. The shallow depth of field is a desired trait in some situations, such as portrait photography, but here it is actively working against the user.
Edit: The same, by the way, applies to macro. An A7S III with a Canon EF 100mm lens has the same AoV and pixel count as a TG-6, and while its much larger sensor (30x more area) will resolve a lot more detail, the TG-6 will get a lot more of that same shot in focus - the FF camera will have to do focus stacking to match the TG-6 shot.