The first stars that formed after the Big Bang were probably massive, and they provided the Universe with the first elements heavier than helium ('metals'), which were incorporated into low-mass stars that have survived to the present. Eight stars in the oldest globular cluster in the Galaxy, NGC 6522, were found to have surface abundances consistent with the gas from which they formed being enriched by massive stars (that is, with higher α-element/Fe and Eu/Fe ratios than those of the Sun). However, the same stars have anomalously high abundances of Ba and La with respect to Fe, which usually arises through nucleosynthesis in low-mass stars (via the slow-neutron-capture process, or s-process). Recent theory suggests that metal-poor fast-rotating massive stars are able to boost the s-process yields by up to four orders of magnitude, which might provide a solution to this contradiction. Here we report a reanalysis of the earlier spectra, which reveals that Y and Sr are also overabundant with respect to Fe, showing a large scatter similar to that observed in extremely metal-poor stars, whereas C abundances are not enhanced. This pattern is best explained as originating in metal-poor fast-rotating massive stars, which might point to a common property of the first stellar generations and even of the 'first stars'.