Subduction initiation is a key in understanding the dynamic evolution of the Earth and its fundamental difference to all other rocky planetary bodies in our solar system. Despite recent progress, the question about how a stiff, mostly stagnant planetary lid can break and become part in the global overturn of the mantle is still unresolved. Many mechanisms, externally or internally driven, are proposed in previous studies. Here, we present the results on subduction initiation obtained by dynamically self-consistent, time-dependent numerical modelling of mantle convection. We show that the stress distribution and resulting deformation of the lithosphere are strongly controlled by the top boundary formulation: A free surface enables surface topography and plate bending, increases gravitational sliding of the plates and leads to more realistic, lithosphere-scale shear zones. As a consequence, subduction initiation induced by regional mantle flow is demonstrably favoured by a free surface compared to the commonly applied, vertically fixed (i.e. free-slip) surface. In addition, we present global, three-dimensional mantle convection experiments that employ basal heating that leads to narrow mantle plumes. Narrow mantle plumes impinging on the base of the plate cause locally weak plate segments and a large topography at the lithosphere-asthenosphere boundary. Both are shown to be key to induce subduction initiation. Finally, our model self-consistently reproduces an episodic lid with a fast global overturn due to the hotter mantle developed below a former stagnant lid. We conclude that once in a stagnant-lid mode, a planet (like Venus) might preferentially evolve by temporally discrete, global overturn events rather than by a continuous recycling of lid and that this is something worth testing more rigorously in future studies.