We study the formation of primordial continental crust (TTG rocks) employing fully self-consistent numerical models of thermochemical convection on a global scale. Starting from a pyrolytic bulk composition and an initially hot core, we first generate oceanic crust and depleted mantle. In our model, the basaltic material is both erupted at the surface and intruded at the base of the crust following a predefined partitioning. Second, we track the pressure-temperature conditions of the newly formed hydrated basalt and check whether it matches the conditions necessary for the formation of primordial continental crust. We show that the “heat-pipe” model (assuming 100% eruption and no intrusion) proposed to be the main heat loss mechanism during the Archean epoch [Moore & Webb 2013] is not able to produce continental crust since it forms a cold and thick lithosphere. We systematically test various mechanical properties of the brittle domain (friction coefficients). Using our parameter study, we are also able to show that an intrusion fraction close to 70% (in agreement with [Crisp 1984]) combined with a friction coefficient of 0.2 produces the expected amount of the three main petrological TTG compositions previously reported [Moyen 2011].