The Kuramoto model is a prototypical model used for rigorous mathematical analysis in the field of synchronization and nonlinear dynamics. A realisation of this model consists of a collection of identical oscillators with interactions given by a network. The Kuramoto dynamics then follows a gradient flow on a network-dependent energy function. We investigate how does the topology of massive networks influence the landscape of the energy function, in particular to the appearance of spurious local minima. We show that if the network is sufficiently expanding (that is, information spreads quickly), then no spurious minima can occur.