Colloidal Laves phases (LPs) of $MgCu_2$ type are promising precursors for diamond structure photonic materials. They have been predicted for hard sphere binary mixtures, but not yet observed. We here report a time resolved static light scattering study on their formation in a binary mixture of buoyant experimental hard sphere approximants (size ratio $Gamma=0.77$, molar fraction of small spheres $x_S = 0.76$) for volume fractions between melting and the glass transition. In line with theoretical expectation, all samples form LPs of $MgZn_2$ structure on the time scale of weeks to months. $MgNi_2$ structures are absent, $MgCu_2$ structures and randomly stacked LPs prevail at elevated volume fraction. The addition of small amounts of non-adsorbing polymer switches the interaction to depletion attractive and results in significantly accelerated crystallization kinetics and improved crystal quality.