Recent attempts to detect [OIII] 88$\mu$m emission from super-early ($z>10$)galaxy candidates observed by JWST have been unsuccessful. By using zoom-insimulations, we show that these galaxies are faint, and mostly fall below thelocal metal-poor $\rm [OIII]-SFR$ relation as a result of their low ionizationparameter, $U_{\rm ion}\lesssim 10^{-3}$. Such low $U_{\rm ion}$ values arefound in galaxies that are in an early assembly stage, and whose stars arestill embedded in high-density natal clouds. However, the most luminous galaxyin our sample ($\rm{log}[L_{\rm{[OIII]}}/L_\odot] = 8.4$, $U_{\rm ion} \approx0.1$) could be detected by ALMA in only $2.8$ hrs.