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Compact groups of dwarf galaxies (CGDs) have been observed at low redshifts (z < 0.1) and are direct evidence of hierarchical assembly at low masses. To understand the formation of CGDs and the galaxy assembly in the low-mass regime, we search for analogues of compact (radius ≤100 kpc) groups of dwarfs (7 ≤ log [ M */M⊙] ≤ 9.5) in the IllustrisTNG highest resolution simulation. Our analysis shows that TNG50-1 can successfully produce CGDs at z  = 0 with realistic total and stellar masses. We also find that the CGD number density decreases towards the present, especially at z ≲ 0.26, reaching |$n \approx 10^{-3.5} \ \rm cMpc^{-3}$| at z  = 0. This prediction can be tested observationally with upcoming surveys targeting the faint end of the galaxy population and is essential to constrain galaxy evolution models in the dwarf regime. The majority of simulated groups at z ∼ 0 formed recently (⁠|$\lesssim 1.5 \ \rm Gyr$|⁠), and CGDs identified at z ≤ 0.5 commonly take more than 1 Gyr to merge completely, giving origin to low- to intermediate-mass (8 ≤ log [ M */M⊙] ≤ 10) normally star-forming galaxies at z  = 0. We find that haloes hosting CGDs at z  = 0 formed later when compared to haloes of similar mass, having lower stellar masses and higher total gas fractions. The simulations suggest that CGDs observed at z ∼ 0 arise from a late hierarchical assembly in the last ∼3 Gyr, producing rapid growth in total mass relative to stellar mass and creating dwarf groups with median halo masses of |$\sim 10^{11.3} \ \rm M_\odot$| and B -band mass-to-light ratios mostly in the range 10 ≲ M / L ≲ 100, in agreement with previous theoretical and observational studies. [ABSTRACT FROM AUTHOR]