  Leading theories for the presence of plate tectonics on Earth typically
appeal to the role of present day conditions in promoting rheological weakening
of the lithosphere. However, it is unknown whether the conditions of the early
Earth were favorable for plate tectonics, or any form of subduction, and thus
how subduction begins is unclear. Using physical models based on grain-damage,
a grainsize-feedback mechanism capable of producing plate-like mantle
convection, we demonstrate that subduction was possible on the Hadean Earth
(hereafter referred to as proto-subduction or proto-plate tectonics), that
proto-subduction differed from modern day plate tectonics, and that it could
initiate rapidly. Scaling laws for convection with grain-damage show that,
though either higher mantle temperatures or higher surface temperatures lead to
slower plates, proto-subduction, with plate speeds of $\approx 1.75$ cm/yr, can
still be maintained in the Hadean, even with a CO$_2$ rich primordial
atmosphere. Furthermore, when the mantle potential temperature is high (e.g.
above $\approx 2000$ K), the mode of subduction switches to a "sluggish
subduction" style, where downwellings are drip-like and plate boundaries are
diffuse. Finally, numerical models of post-magma ocean mantle convection
demonstrate that proto-plate tectonics likely initiates within $\sim100$ Myrs
of magma ocean solidification, consistent with evidence from Hadean zircons.
After the initiation of proto-subduction, non-plate-tectonic "sluggish
subduction" prevails, giving way to modern style plate tectonics as both the
mantle interior and climate cool. Hadean proto-subduction may hasten the onset
of modern plate tectonics by drawing excess CO$_2$ out of the atmosphere and
cooling the climate.
