The Λ cold dark matter (ΛCDM) paradigm of galaxy formation predicts that dense spheroidal stellar structures invariably grow at early cosmic time. These primordial spheroids evolve toward a virialized dynamical status as they finally become today's elliptical galaxies and large bulges at the center of disk galaxies. However, observations reveal that small bulges in spiral galaxies are common in the nearby universe. The prevailing belief that all small bulges form at later times from internal processes occurring in the disk represents a challenge for the ΛCDM scenario. Notably, the coevolution of bulges and central supermassive black holes (SMBHs) at early phases of galaxy evolution is also at stake. However, observations have so far not provided conclusive evidence against their possible early origin. Here, we report new observations of small bulges showing that they follow the mass─velocity dispersion relation expected for virialized systems. Contrary to previous claims, small bulges bridge the gap between massive ellipticals and globular clusters. This dynamical picture supports a scenario where systems over seven orders of magnitude in stellar mass form at early cosmic time. These results alleviate the tension between ΛCDM simulations and observations at galactic scales. We hypothesize that these small bulges are actually the low-mass descendants of compact objects observed at high redshift, also known as red nuggets, which are consistently produced in cosmological ΛCDM simulations. Therefore, this also suggests that the established coevolution of SMBHs and large bulges naturally extends to spheroids in the low-mass regime.