We present Atacama Large Millimetre/submillimetre Array (ALMA) observations of the [O iii] 88 μm 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 > 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 $\rm {\rm M}_{\odot }/yr$. 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 > 6 Universe ($L_\mathrm{[O\, \small {III}]}/L_\mathrm{[C\, \small {II}]}$ < 1.2 at 3σ). 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 (<141μJy at 3σ), implies a low average dust temperature (Tdust ≲ 30 K) and high dust mass (Mdust ∼ 108 M⊙). 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.