At cosmic dawn, the 21-centimeter signal from intergalactic hydrogen was driven by Lyman-$\alpha$ photons from some of the earliest stars, producing a spatial pattern that reflected the distribution of galaxies at that time. Due to the large foreground, it is thought that around redshift 20 it is only observationally feasible to detect 21-cm fluctuations statistically, yielding a limited, indirect probe of early galaxies. Here we show that 21-cm images at cosmic dawn should actually be dominated by large (tens of comoving megaparsecs), high contrast bubbles surrounding individual galaxies. We demonstrate this using a substantially upgraded semi-numerical simulation code that realistically captures the formation and 21-cm effects of the small galaxies expected during this era. Small number statistics associated with the rarity of early galaxies, combined with the multiple scattering of photons in the blue wing of the Lyman-$\alpha$ line, create the large bubbles and also enhance the 21-cm power spectrum by a factor of 2--7 and add to it a feature that measures the typical brightness of galaxies. These various signatures of discrete early galaxies are potentially detectable with planned experiments such as the Square Kilometer Array or the Hydrogen Epoch of Reionization Array, even if the early stars formed in dark matter halos with masses as low as $108M\odot$, ten thousand times smaller than the Milky Way halo.