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ABSTRACT Disentangling distinct stellar populations along the red-giant branches (RGBs) of globular clusters (GCs) is possible by using the pseudo-two-colour diagram dubbed chromosome map (ChM). One of the most intriguing findings is that the so-called first-generation (1G) stars, characterized by the same chemical composition of their natal cloud, exhibit extended sequences in the ChM. Unresolved binaries and internal variations in helium or metallicity have been suggested to explain this phenomenon. Here, we derive high-precision Hubble Space Telescope photometry of the GCs NGC 6362 and NGC 6838 and build their ChMs. We find that both 1G RGB and main-sequence (MS) stars exhibit wider ChM sequences than those of second-generation (2G). The evidence of this feature even among unevolved 1G MS stars indicates that chemical inhomogeneities are imprinted in the original gas. We introduce a pseudo-two-magnitude diagram to distinguish between helium and metallicity, and demonstrate that star-to-star metallicity variations are responsible for the extended 1G sequence. Conversely, binaries provide a minor contribution to the phenomenon. We estimate that the metallicity variations within 1G stars of 55 GCs range from less than [Fe/H]∼0.05 to ∼0.30 and mildly correlate with cluster mass. We exploit these findings to constrain the formation scenarios of multiple populations showing that they are qualitatively consistent with the occurrence of multiple generations. In contrast, the fact that 2G stars have more homogeneous iron content than the 1G challenges the scenarios based on accretion of material processed in massive 1G stars on to existing protostars.