ABSTRACT We present Atacama Large Millimetre/submillimetre Array (ALMA) observations of the [O iii] 88 $\mu {\rm m}$ emission of a sample of thirteen galaxies at $z = 6$ to 7.6 selected as [C ii]-emitting companion sources of quasars. To disentangle the origins of the luminous Oxygen line in the $z\, \gt\, 6$ Universe, we looked at emission-line galaxies that are selected through an excellent star-formation tracer [C ii] with star-formation rates between 9 and 162 $\rm {\rm M}_{\odot }\,yr^{-1}$. Direct observations reveal [O iii] emission in just a single galaxy ($L_\mathrm{[O\, {\small III}]}/L_\mathrm{[C\, {\small II}]}$$\, = 2.3$), and a stacked image shows no [O iii] detection, providing deep upper limits on the $L_\mathrm{[O\, {\small III}]}/L_\mathrm{[C\, {\small II}]}$ ratios in the $z \gt 6$ Universe ($L_\mathrm{[O\, {\small III}]}/L_\mathrm{[C\, {\small II}]}$$\, \lt 1.2$ at $3 \sigma$). While the fidelity of this sample is high, no obvious optical/near-infrared counterpart is seen in the JWST imaging available for four galaxies. Additionally accounting for low-z CO emitters, line stacking shows that our sample-wide result remains robust: The enhanced $L_\mathrm{[O\, {\small III}]}/L_\mathrm{[C\, {\small II}]}$ reported in the first billion years of the Universe is likely due to the selection towards bright, blue Lyman-break galaxies with high surface star-formation rates or young stellar populations. The deep upper limit on the rest-frame 90 μm continuum emission ($\lt 141 \mu$Jy at $3 \sigma$), implies a low average dust temperature ($T_\mathrm{dust} \lesssim 30\,$ K) and high-dust mass ($M_\mathrm{dust} \sim 10^8\, \mathrm{M}_\odot$). As more normal galaxies are explored in the early Universe, synergy between JWST and ALMA is fundamental to further investigate the ISM properties of the a broad range of samples of high-z galaxies.