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Abstract Despite significant study, when and how plate tectonics initiated on Earth remains contentious. Geologic evidence from some of Earth's earliest cratons has been interpreted as reflecting the formation of initial continental blocks by non‐subduction processes, which then trigger subduction initiation at their margins. Numerical models of mantle convection with a plastic yield stress rheology have shown this scenario is plausible. However, whether continents can trigger subduction initiation has not been tested with other rheologies. We, therefore, use numerical models of mantle convection with an imposed continental block to test whether continents facilitate subduction initiation with a grain‐damage mechanism, where weak shear zones form by grain size reduction. Our results show that continents modestly enhance stresses in the lithosphere, but not enough to significantly impact lithospheric damage or subduction initiation: continents have minimal influence on lithospheric damage or plate speed, nor does subduction preferentially initiate at the continental margin. A new regime diagram that includes continental blocks shows only a small shift in the boundary between the mobile‐lid and stagnant‐lid regimes when continents are added. However, as we do find that stresses are modestly enhanced at the continental margin in our models, we develop a scaling law for this stress enhancement to more fully test whether continents could trigger subduction initiation on early Earth. We find that lithospheric stresses supplied by continents are not sufficient to initiate subduction on the early Earth on their own with grain‐damage rheology; instead, additional factors would be required.