The Barnard 1b core shows signatures of being at the earliest stages of low-mass star formation, with two extremely young and deeply embedded proto-stellar objects. Hence, this core is an ideal target to study the structure and chemistry of the first objects formed in the collapse of prestellar cores. We present ALMA Band 6 spectral line observations at ~0.6″ of angular resolution towards Barnard 1b. We have extracted the spectra towards both protostars, and used a local thermodynamic equilibrium (LTE) model to reproduce the observed line profiles. B1b-S shows rich and complex spectra, with emission from high energy transitions of complex molecules, such as CH₃OCOH and CH₃CHO, including vibrational level transitions. We have tentatively detected for the first time in this source emission from NH₂CN, NH₂CHO, CH₃CH₂OH, CH₂OHCHO, CH₃CH₂OCOH and both aGg′ and gGg′ conformers of (CH₂OH)₂. This is the first detection of ethyl formate (CH₃CH₂OCOH) towards a low-mass star forming region. On the other hand, the spectra of the FHSC candidate B1b-N are free of COMs emission. In order to fit the observed line profiles in B1b-S, we used a source model with two components: an inner hot and compact component (200 K, 0.35″) and an outer and colder one (60 K, 0.6″). The resulting COM abundances in B1b-S range from 10⁻¹³ for NH₂CN and NH₂CHO, up to 10⁻⁹ for CH₃OCOH. Our ALMA Band 6 observations reveal the presence of a compact and hot component in B1b-S, with moderate abundances of complex organics. These results indicate that a hot corino is being formed in this very young Class 0 source.