Using first-principles combined with quantum transport calculations, we predict that graphene sandwiched between insulating monolayers of Cr₂Ge₂Te₆ ferromagnet and WS₂ transition-metal dichalcogenide will exhibit spin-orbit torque (SOT) when unpolarized charge current is injected parallel to interfaces of Cr₂Ge₂Te₆/graphene/WS₂ van der Waals (vdW) heterostructure. Although graphene by itself is nonmagnetic and it has negligible spin-orbit coupling (SOC), both of which are required for the SOT phenomenon, Cr₂Ge₂Te₆ induces proximity magnetism into graphene while WS₂ concurrently imprints valley-Zeeman and Rashba SOCs in it. Unlike SOT on conventional metallic ferromagnets brought into contact with normal materials supplying strong SOC, the predicted SOT on such doubly proximitized graphene can be tuned by up to two orders of magnitude via combined top and back electrostatic gates. The vdW heterostructure also reveals how damping-like component of the SOT vector can arise purely from interfaces and, therefore, even in the absence of any spin Hall current from the bulk of a material with strong SOC. The SOT-driven dynamics of proximity magnetization moves it from out-of-plane to in-plane direction which opens a gap in graphene and leads to zero off current and diverging on/off ratio in such SOT field-effect transistor.