Observations of anisotropies in the brightness temperature of the 21 cm line of neutral hydrogen from the period before reionization would shed light on the dawn of the first stars and galaxies. In this paper, we use large-scale semi-numerical simulations to analyse the imprint on the 21 cm signal of spatial fluctuations in the Lyman-alpha flux arising from the clustering of the first galaxies. We show that an experiment such as the Square Kilometer Array (SKA) can probe this signal at the onset of reionization, giving us important information about the UV emission spectra of the first stars and characterizing their host galaxies. SKA-pathfinders with ~10% of the full collecting area should be capable of making a statistical detection of the 21 cm power spectrum at redshifts z ≲ 20 (corresponding to frequencies nu ≳ 67 MHz). We then show that the SKA should be able to measure the three dimensional power spectrum as a function of the angle with the line of sight and discuss the use of the redshift space distortions as a way to separate out the different components of the 21 cm power spectrum. We demonstrate that, at least on large scales where the Lyalpha fluctuations are linear, they can be used as a model independent way to extract the power spectra due to these Lyalpha fluctuations.