How did the tectonic plates first form?
no one knows the theory is that convection currents in the mantle formed the plates.
The crust may have started as cooled igneous material from the surface of the mantle. The surface would have hardened as it cooled to form one giant crustal plate.
The mantle underneath this newly formed crust would still be churning and turning in the convection currents. At places the convection currents would bring new crustal material up from the mantle. The upthrusting current would break the crust into two pieces. At other places the cooling mantle would drag the attached crust down as the cooling mantle material being more dense would sink back down into the hotter magma beneath. The downward movement of the mantle would create subduction zones causing a second break in the crust.
The theory of plate tectonics provides a reasonable explanation of how the plates might have formed from the action of convection currents in the hot magma of the mantle. How the crustal plates first formed in not known for certain however.