We analysed the Atacama Large Millimetre/submillimetre Array (ALMA) far-infrared (FIR), 1.3 mm, dust continuum and CO emission of 12 starburst galaxies at $z 2.1-3.6$ selected for their extreme brightness in the rest-frame UV, with absolute magnitudes of $-23.4$ to $-24.7$. We also analysed their Very Large Telescope (VLT) High Acuity Wide field $K$-band Imager (HAWK-I) $H$- and s $-band images. The targeted galaxies are characterised by negligible dust attenuations with blue UV spectral slopes ($-2.62$ to $-1.84$), very young stellar populations of $ 10$ Myr, and powerful starbursts with a high mean specific star-formation rate of $ $, placing them $ 1.5$ dex above the main sequence at similar redshifts and stellar masses stars odot $). The FIR dust continuum emission revealed in nine galaxies gives IR luminosities of $(5.9-28.3) L_ odot $, with six galaxies remaining dominated by unobscured UV star-formation rates, and high dust masses barely produced by supernovae within the 10 Myr timescale. The CO emission detected in eight galaxies leads to molecular gas masses higher than stellar masses, with the mean molecular gas mass fraction as high as $82<!PCT!>$. The corresponding star-formation efficiencies reach $ 40$<!PCT!>, with amazingly short molecular gas depletion timescales between less than 13 Myr and 71 Myr. These unique properties never reported in previously studied galaxies highlight that these galaxies are likely caught at the very beginning of their stellar mass build-up and undergo a very efficient and fast conversion of gas into stars that can only result from the gas collapse within a very short free-fall time. We find that the feedback-free starburst model seems to be able to explain the formation of these galaxies. To reconcile the co-spatial FIR dust emission with the UV-bright unattenuated emission, we speculate about the presence of radiation-driven outflows that can temporarily remove dust at the location of the starburst and expel it at large distances in line with the measured high FIR effective radii (1.7 kpc to 5 kpc) in comparison to the very compact stellar radii that are a few hundreds of parsecs).
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