In the last decade, growing evidence has emerged supporting a non-universal stellar initial mass function (IMF) in massive galaxies, with a larger number of dwarf stars with respect to the Milky Way (bottom-heavy IMF). However, a consensus about the mechanisms that cause IMF variations is yet to be reached. Recently, it has been suggested that stars formed early-on in cosmic time, via a star formation burst, could be characterized by a bottom-heavy IMF. A promising way to confirm this is to use relics, ultra-compact massive galaxies, almost entirely composed by these ‘pristine’ stars. The INvestigating Stellar Population In RElics (INSPIRE) Project aims at assembling a large sample of confirmed relics, that can serve as laboratory to investigate on the conditions of star formation in the first 1–3 Gyr of the Universe. In this third INSPIRE paper, we build a high signal-to-noise spectrum from five relics, and one from five galaxies with similar sizes, masses, and kinematical properties, but characterized by a more extended star formation history (non-relics). Our detailed stellar population analysis suggests a systematically bottom-heavier IMF slope for relics than for non-relics, adding new observational evidence for the non-universality of the IMF at various redshifts and further supporting the above proposed physical scenario.