Observations of massive stars within the central parsec of the Galaxy show that, while most stars orbit within a well-defined disc, a significant fraction have large eccentricities and / or inclinations with respect to the disc plane. Here, we investigate whether this dynamically hot component could have arisen via scattering from an initially cold disc - the expected initial condition if the stars formed from the fragmentation of an accretion disc. Using N-body methods, we evolve a variety of flat, cold, stellar systems, and study the effects of initial disc eccentricity, primordial binaries, very massive stars and intermediate mass black holes. We find, consistent with previous results, that a circular disc does not become eccentric enough unless there is a significant population of undetected 100-1000 \msun objects. However, since fragmentation of an eccentric disc can readily yield eccentric stellar orbits, the strongest constraints come from inclinations. We show that none of our initial conditions yield the observed large inclinations, regardless of the initial disc eccentricity or the presence of massive objects. These results imply that the orbits of the young massive stars in the Galactic Centre are largely primordial, and that the stars are unlikely to have formed as a dynamically cold disc.